%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO249^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:47:17 AM UTC 2026
% Result : Theorem 2.65s 0.79s
% Output : Refutation 2.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO249^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n018.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 16:43:26 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 Running higher-order theorem proving
% 0.10/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.39/0.40 % (320849)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.39/0.40 % (320857)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2249034518:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.39/0.40 % (320854)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3835573081:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.39/0.40 % (320855)lrs+10_16_si=on:nwc=1.5:random_seed=4274471426:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.39/0.40 % (320860)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.39/0.40 % (320860)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.39/0.40 % (320855)Instruction limit reached!
% 0.39/0.40 % (320855)------------------------------
% 0.39/0.40 % (320855)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.40 % (320855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.40 % (320855)CaDiCaL version: 2.1.3
% 0.39/0.40 % (320855)Termination reason: Instruction limit
% 0.39/0.40 % (320855)Termination phase: Saturation
% 0.39/0.40 % (320855)Time elapsed: 0.011 s
% 0.39/0.40 % (320855)Peak memory usage: 12 MB
% 0.39/0.40 % (320855)Instructions burned: 19 (million)
% 0.39/0.40 % (320859)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3578012263:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.39/0.40 % (320856)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3289487416:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.39/0.40 % (320858)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3187265932:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.39/0.40 % (320856)Instruction limit reached!
% 0.39/0.40 % (320856)------------------------------
% 0.39/0.40 % (320856)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.40 % (320856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.40 % (320856)CaDiCaL version: 2.1.3
% 0.39/0.40 % (320856)Termination reason: Instruction limit
% 0.39/0.40 % (320856)Termination phase: Property scanning
% 0.39/0.40 % (320856)Time elapsed: 0.002 s
% 0.39/0.40 % (320856)Peak memory usage: 11 MB
% 0.39/0.40 % (320856)Instructions burned: 5 (million)
% 0.39/0.40 % (320860)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1247722535:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.39/0.40 % (320864)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3122909941:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.39/0.40 % (320864)Instruction limit reached!
% 0.39/0.40 % (320864)------------------------------
% 0.39/0.40 % (320864)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.40 % (320864)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.40 % (320864)CaDiCaL version: 2.1.3
% 0.39/0.40 % (320864)Termination reason: Instruction limit
% 0.39/0.40 % (320864)Termination phase: Saturation
% 0.39/0.40 % (320864)Time elapsed: 0.003 s
% 0.39/0.40 % (320864)Peak memory usage: 11 MB
% 0.39/0.40 % (320864)Instructions burned: 5 (million)
% 0.39/0.40 % (320854)Instruction limit reached!
% 0.39/0.40 % (320854)------------------------------
% 0.39/0.40 % (320854)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.40 % (320854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.40 % (320854)CaDiCaL version: 2.1.3
% 0.39/0.40 % (320854)Termination reason: Instruction limit
% 0.39/0.40 % (320854)Termination phase: Saturation
% 0.39/0.40 % (320854)Time elapsed: 0.044 s
% 0.39/0.40 % (320854)Peak memory usage: 13 MB
% 0.39/0.40 % (320854)Instructions burned: 88 (million)
% 0.39/0.40 % (320858)Instruction limit reached!
% 0.39/0.40 % (320858)------------------------------
% 0.39/0.40 % (320858)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.40 % (320858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.43 % (320858)CaDiCaL version: 2.1.3
% 0.94/0.43 % (320858)Termination reason: Instruction limit
% 0.94/0.43 % (320858)Termination phase: Saturation
% 0.94/0.43 % (320858)Time elapsed: 0.028 s
% 0.94/0.43 % (320858)Peak memory usage: 12 MB
% 0.94/0.43 % (320858)Instructions burned: 26 (million)
% 0.94/0.43 % (320871)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.94/0.43 % (320871)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2817765334:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.94/0.43 % (320869)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2725602373:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.94/0.43 % (320872)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1514217396:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.94/0.43 % (320869)Instruction limit reached!
% 0.94/0.43 % (320869)------------------------------
% 0.94/0.43 % (320869)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.43 % (320869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.43 % (320869)CaDiCaL version: 2.1.3
% 0.94/0.43 % (320869)Termination reason: Instruction limit
% 0.94/0.43 % (320869)Termination phase: Saturation
% 0.94/0.43 % (320869)Time elapsed: 0.003 s
% 0.94/0.43 % (320869)Peak memory usage: 11 MB
% 0.94/0.43 % (320869)Instructions burned: 6 (million)
% 0.94/0.43 % (320871)Instruction limit reached!
% 0.94/0.43 % (320871)------------------------------
% 0.94/0.43 % (320871)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.43 % (320871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.43 % (320871)CaDiCaL version: 2.1.3
% 0.94/0.43 % (320871)Termination reason: Instruction limit
% 0.94/0.43 % (320871)Termination phase: Saturation
% 0.94/0.43 % (320871)Time elapsed: 0.004 s
% 0.94/0.43 % (320871)Peak memory usage: 12 MB
% 0.94/0.43 % (320871)Instructions burned: 8 (million)
% 0.94/0.43 % (320872)Instruction limit reached!
% 0.94/0.43 % (320872)------------------------------
% 0.94/0.43 % (320872)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.43 % (320872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.43 % (320872)CaDiCaL version: 2.1.3
% 0.94/0.43 % (320872)Termination reason: Instruction limit
% 0.94/0.43 % (320872)Termination phase: Saturation
% 0.94/0.43 % (320872)Time elapsed: 0.007 s
% 0.94/0.43 % (320872)Peak memory usage: 12 MB
% 0.94/0.43 % (320872)Instructions burned: 13 (million)
% 0.94/0.43 % (320873)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.94/0.43 % (320873)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.94/0.43 % (320873)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3903165183:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.94/0.43 % (320859)Instruction limit reached!
% 0.94/0.43 % (320859)------------------------------
% 0.94/0.43 % (320859)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.43 % (320859)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.43 % (320859)CaDiCaL version: 2.1.3
% 0.94/0.43 % (320859)Termination reason: Instruction limit
% 0.94/0.43 % (320859)Termination phase: Saturation
% 0.94/0.43 % (320859)Time elapsed: 0.069 s
% 0.94/0.43 % (320859)Peak memory usage: 13 MB
% 0.94/0.43 % (320859)Instructions burned: 75 (million)
% 0.94/0.43 % (320878)lrs+10_1_si=on:cs=on:random_seed=3669937674:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.94/0.43 % (320878)Instruction limit reached!
% 0.94/0.43 % (320878)------------------------------
% 0.94/0.43 % (320878)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.43 % (320878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.43 % (320878)CaDiCaL version: 2.1.3
% 0.94/0.43 % (320878)Termination reason: Instruction limit
% 0.94/0.46 % (320878)Termination phase: Saturation
% 0.94/0.46 % (320878)Time elapsed: 0.005 s
% 0.94/0.46 % (320878)Peak memory usage: 12 MB
% 0.94/0.46 % (320878)Instructions burned: 9 (million)
% 0.94/0.46 % (320879)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.94/0.46 % (320877)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=234359249:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.94/0.46 % (320882)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3082200883:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.94/0.46 % (320873)Instruction limit reached!
% 0.94/0.46 % (320873)------------------------------
% 0.94/0.46 % (320873)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.46 % (320873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.46 % (320873)CaDiCaL version: 2.1.3
% 0.94/0.46 % (320873)Termination reason: Instruction limit
% 0.94/0.46 % (320873)Termination phase: Saturation
% 0.94/0.46 % (320873)Time elapsed: 0.028 s
% 0.94/0.46 % (320873)Peak memory usage: 12 MB
% 0.94/0.46 % (320873)Instructions burned: 29 (million)
% 0.94/0.46 % (320879)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=3863384234:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.94/0.46 % (320879)Instruction limit reached!
% 0.94/0.46 % (320879)------------------------------
% 0.94/0.46 % (320879)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.46 % (320879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.46 % (320879)CaDiCaL version: 2.1.3
% 0.94/0.46 % (320879)Termination reason: Instruction limit
% 0.94/0.46 % (320879)Termination phase: Saturation
% 0.94/0.46 % (320879)Time elapsed: 0.002 s
% 0.94/0.46 % (320879)Peak memory usage: 11 MB
% 0.94/0.46 % (320879)Instructions burned: 4 (million)
% 0.94/0.46 % (320883)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=114076127:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.94/0.46 % (320888)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=4238911311:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.94/0.46 % (320882)Instruction limit reached!
% 0.94/0.46 % (320882)------------------------------
% 0.94/0.46 % (320882)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.46 % (320882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.46 % (320882)CaDiCaL version: 2.1.3
% 0.94/0.46 % (320882)Termination reason: Instruction limit
% 0.94/0.46 % (320882)Termination phase: Saturation
% 0.94/0.46 % (320882)Time elapsed: 0.028 s
% 0.94/0.46 % (320882)Peak memory usage: 12 MB
% 0.94/0.46 % (320882)Instructions burned: 38 (million)
% 0.94/0.46 % (320888)Instruction limit reached!
% 0.94/0.46 % (320888)------------------------------
% 0.94/0.46 % (320888)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.46 % (320888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.46 % (320888)CaDiCaL version: 2.1.3
% 0.94/0.46 % (320888)Termination reason: Instruction limit
% 0.94/0.46 % (320888)Termination phase: Saturation
% 0.94/0.46 % (320888)Time elapsed: 0.008 s
% 0.94/0.46 % (320888)Peak memory usage: 12 MB
% 0.94/0.46 % (320888)Instructions burned: 14 (million)
% 0.94/0.46 % (320877)Instruction limit reached!
% 0.94/0.46 % (320877)------------------------------
% 0.94/0.46 % (320877)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.94/0.46 % (320877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.94/0.46 % (320877)CaDiCaL version: 2.1.3
% 0.94/0.46 % (320877)Termination reason: Instruction limit
% 0.94/0.46 % (320877)Termination phase: Saturation
% 0.94/0.46 % (320877)Time elapsed: 0.038 s
% 0.94/0.46 % (320877)Peak memory usage: 12 MB
% 0.94/0.46 % (320877)Instructions burned: 86 (million)
% 0.94/0.46 % (320886)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2045751038:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.94/0.46 % (320891)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3855337522:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.78/0.54 % (320857)Instruction limit reached!
% 1.78/0.54 % (320857)------------------------------
% 1.78/0.54 % (320857)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.78/0.54 % (320857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.78/0.54 % (320857)CaDiCaL version: 2.1.3
% 1.78/0.54 % (320857)Termination reason: Instruction limit
% 1.78/0.54 % (320857)Termination phase: Saturation
% 1.78/0.54 % (320857)Time elapsed: 0.161 s
% 1.78/0.54 % (320857)Peak memory usage: 15 MB
% 1.78/0.54 % (320857)Instructions burned: 636 (million)
% 1.78/0.54 % (320860)Instruction limit reached!
% 1.78/0.54 % (320860)------------------------------
% 1.78/0.54 % (320860)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.78/0.54 % (320860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.78/0.54 % (320860)CaDiCaL version: 2.1.3
% 1.78/0.54 % (320860)Termination reason: Instruction limit
% 1.78/0.54 % (320860)Termination phase: Saturation
% 1.78/0.54 % (320860)Time elapsed: 0.135 s
% 1.78/0.54 % (320860)Peak memory usage: 13 MB
% 1.78/0.54 % (320860)Instructions burned: 157 (million)
% 1.78/0.54 % (320892)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=607007865:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.78/0.54 % (320893)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=3920235538:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.78/0.54 % (320893)Instruction limit reached!
% 1.78/0.54 % (320893)------------------------------
% 1.78/0.54 % (320893)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.78/0.54 % (320893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.78/0.54 % (320893)CaDiCaL version: 2.1.3
% 1.78/0.54 % (320893)Termination reason: Instruction limit
% 1.78/0.54 % (320893)Termination phase: Saturation
% 1.78/0.54 % (320893)Time elapsed: 0.003 s
% 1.78/0.54 % (320893)Peak memory usage: 12 MB
% 1.78/0.54 % (320893)Instructions burned: 6 (million)
% 1.78/0.54 % (320892)Instruction limit reached!
% 1.78/0.54 % (320892)------------------------------
% 1.78/0.54 % (320892)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.78/0.54 % (320892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.78/0.54 % (320892)CaDiCaL version: 2.1.3
% 1.78/0.54 % (320892)Termination reason: Instruction limit
% 1.78/0.54 % (320892)Termination phase: Saturation
% 1.78/0.54 % (320892)Time elapsed: 0.008 s
% 1.78/0.54 % (320892)Peak memory usage: 12 MB
% 1.78/0.54 % (320892)Instructions burned: 15 (million)
% 1.78/0.54 % (320896)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3686788694:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.78/0.54 % (320886)Instruction limit reached!
% 1.78/0.54 % (320886)------------------------------
% 1.78/0.54 % (320886)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.78/0.54 % (320886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.78/0.54 % (320886)CaDiCaL version: 2.1.3
% 1.78/0.54 % (320886)Termination reason: Instruction limit
% 1.78/0.54 % (320886)Termination phase: Saturation
% 1.78/0.54 % (320886)Time elapsed: 0.023 s
% 1.78/0.54 % (320886)Peak memory usage: 12 MB
% 1.78/0.54 % (320886)Instructions burned: 25 (million)
% 1.78/0.54 % (320898)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=4238315232:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.78/0.54 % (320901)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.78/0.54 % (320901)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.78/0.54 % (320896)Instruction limit reached!
% 1.78/0.54 % (320896)------------------------------
% 1.78/0.54 % (320896)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.78/0.54 % (320896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.78/0.54 % (320896)CaDiCaL version: 2.1.3
% 1.78/0.54 % (320896)Termination reason: Instruction limit
% 1.78/0.54 % (320896)Termination phase: Saturation
% 1.78/0.62 % (320896)Time elapsed: 0.014 s
% 1.78/0.62 % (320896)Peak memory usage: 12 MB
% 1.78/0.62 % (320896)Instructions burned: 29 (million)
% 1.78/0.62 % (320901)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=821936272:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.78/0.62 % (320905)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=3012532112:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2997 on theBenchmark for (2997ds/31Mi)
% 1.78/0.62 % (320901)Instruction limit reached!
% 1.78/0.62 % (320901)------------------------------
% 1.78/0.62 % (320901)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.78/0.62 % (320901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.78/0.62 % (320901)CaDiCaL version: 2.1.3
% 1.78/0.62 % (320901)Termination reason: Instruction limit
% 1.78/0.62 % (320901)Termination phase: Saturation
% 1.78/0.62 % (320900)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2100654512:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.78/0.62 % (320901)Time elapsed: 0.008 s
% 1.78/0.62 % (320901)Peak memory usage: 12 MB
% 1.78/0.62 % (320901)Instructions burned: 14 (million)
% 1.78/0.62 % (320898)Instruction limit reached!
% 1.78/0.62 % (320898)------------------------------
% 1.78/0.62 % (320898)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.78/0.62 % (320898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.78/0.62 % (320898)CaDiCaL version: 2.1.3
% 1.78/0.62 % (320898)Termination reason: Instruction limit
% 1.78/0.62 % (320898)Termination phase: Saturation
% 1.78/0.62 % (320898)Time elapsed: 0.019 s
% 1.78/0.62 % (320898)Peak memory usage: 12 MB
% 1.78/0.62 % (320898)Instructions burned: 24 (million)
% 1.78/0.62 % (320903)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.78/0.62 % (320905)Instruction limit reached!
% 1.78/0.62 % (320905)------------------------------
% 1.78/0.62 % (320905)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.78/0.62 % (320905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.78/0.62 % (320905)CaDiCaL version: 2.1.3
% 1.78/0.62 % (320905)Termination reason: Instruction limit
% 1.78/0.62 % (320905)Termination phase: Saturation
% 1.78/0.62 % (320905)Time elapsed: 0.008 s
% 1.78/0.62 % (320905)Peak memory usage: 12 MB
% 1.78/0.62 % (320905)Instructions burned: 35 (million)
% 1.78/0.62 % (320903)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=346605791:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.78/0.62 % (320911)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=1962376611:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2997 on theBenchmark for (2997ds/20Mi)
% 1.78/0.62 % (320909)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3969686073:i=7:hud=5:bd=preordered:rtra=on:bet=on_2997 on theBenchmark for (2997ds/7Mi)
% 1.78/0.62 % (320903)Instruction limit reached!
% 1.78/0.62 % (320903)------------------------------
% 1.78/0.62 % (320903)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.78/0.62 % (320903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.78/0.62 % (320903)CaDiCaL version: 2.1.3
% 1.78/0.62 % (320903)Termination reason: Instruction limit
% 1.78/0.62 % (320903)Termination phase: Saturation
% 1.78/0.62 % (320903)Time elapsed: 0.008 s
% 1.78/0.62 % (320903)Peak memory usage: 12 MB
% 1.78/0.62 % (320903)Instructions burned: 8 (million)
% 1.78/0.62 % (320910)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=42722091:i=23:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/23Mi)
% 1.78/0.62 % (320909)Instruction limit reached!
% 1.78/0.62 % (320909)------------------------------
% 1.78/0.62 % (320909)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.78/0.62 % (320909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.78/0.62 % (320909)CaDiCaL version: 2.1.3
% 1.78/0.62 % (320909)Termination reason: Instruction limit
% 1.78/0.62 % (320909)Termination phase: Saturation
% 1.78/0.62 % (320909)Time elapsed: 0.004 s
% 1.78/0.62 % (320909)Peak memory usage: 12 MB
% 2.46/0.70 % (320909)Instructions burned: 8 (million)
% 2.46/0.70 % (320911)Instruction limit reached!
% 2.46/0.70 % (320911)------------------------------
% 2.46/0.70 % (320911)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.70 % (320911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/0.70 % (320911)CaDiCaL version: 2.1.3
% 2.46/0.70 % (320911)Termination reason: Instruction limit
% 2.46/0.70 % (320911)Termination phase: Saturation
% 2.46/0.70 % (320911)Time elapsed: 0.006 s
% 2.46/0.70 % (320911)Peak memory usage: 12 MB
% 2.46/0.70 % (320911)Instructions burned: 23 (million)
% 2.46/0.70 % (320910)Instruction limit reached!
% 2.46/0.70 % (320910)------------------------------
% 2.46/0.70 % (320910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.70 % (320910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/0.70 % (320910)CaDiCaL version: 2.1.3
% 2.46/0.70 % (320910)Termination reason: Instruction limit
% 2.46/0.70 % (320910)Termination phase: Saturation
% 2.46/0.70 % (320910)Time elapsed: 0.009 s
% 2.46/0.70 % (320910)Peak memory usage: 11 MB
% 2.46/0.70 % (320910)Instructions burned: 23 (million)
% 2.46/0.70 % (320917)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=2559358356:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.46/0.70 % (320916)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2133893530:i=1240:rtra=on:ixr=off_2997 on theBenchmark for (2997ds/1240Mi)
% 2.46/0.70 % (320919)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=989500448:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.46/0.70 % (320900)Instruction limit reached!
% 2.46/0.70 % (320900)------------------------------
% 2.46/0.70 % (320900)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.70 % (320900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/0.70 % (320900)CaDiCaL version: 2.1.3
% 2.46/0.70 % (320900)Termination reason: Instruction limit
% 2.46/0.70 % (320900)Termination phase: Saturation
% 2.46/0.70 % (320900)Time elapsed: 0.060 s
% 2.46/0.70 % (320900)Peak memory usage: 12 MB
% 2.46/0.70 % (320900)Instructions burned: 61 (million)
% 2.46/0.70 % (320918)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=2046642204:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.46/0.70 % (320919)Instruction limit reached!
% 2.46/0.70 % (320919)------------------------------
% 2.46/0.70 % (320919)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.70 % (320919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/0.70 % (320919)CaDiCaL version: 2.1.3
% 2.46/0.70 % (320919)Termination reason: Instruction limit
% 2.46/0.70 % (320919)Termination phase: Saturation
% 2.46/0.70 % (320919)Time elapsed: 0.021 s
% 2.46/0.70 % (320919)Peak memory usage: 12 MB
% 2.46/0.70 % (320919)Instructions burned: 42 (million)
% 2.46/0.70 % (320917)Instruction limit reached!
% 2.46/0.70 % (320917)------------------------------
% 2.46/0.70 % (320917)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.70 % (320917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.46/0.70 % (320917)CaDiCaL version: 2.1.3
% 2.46/0.70 % (320917)Termination reason: Instruction limit
% 2.46/0.70 % (320917)Termination phase: Saturation
% 2.46/0.70 % (320917)Time elapsed: 0.040 s
% 2.46/0.70 % (320917)Peak memory usage: 13 MB
% 2.46/0.70 % (320917)Instructions burned: 146 (million)
% 2.46/0.70 % (320926)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=3580523454:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.46/0.70 % (320925)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=768528421:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.46/0.70 % (320924)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.46/0.70 % (320883)Instruction limit reached!
% 2.46/0.70 % (320883)------------------------------
% 2.46/0.70 % (320883)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.46/0.70 % (320883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.79 % (320883)CaDiCaL version: 2.1.3
% 2.65/0.79 % (320883)Termination reason: Instruction limit
% 2.65/0.79 % (320883)Termination phase: Saturation
% 2.65/0.79 % (320883)Time elapsed: 0.182 s
% 2.65/0.79 % (320883)Peak memory usage: 14 MB
% 2.65/0.79 % (320883)Instructions burned: 250 (million)
% 2.65/0.79 % (320924)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1011964942:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.65/0.79 % (320924)Instruction limit reached!
% 2.65/0.79 % (320924)------------------------------
% 2.65/0.79 % (320924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.79 % (320924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.79 % (320924)CaDiCaL version: 2.1.3
% 2.65/0.79 % (320924)Termination reason: Instruction limit
% 2.65/0.79 % (320924)Termination phase: Saturation
% 2.65/0.79 % (320924)Time elapsed: 0.005 s
% 2.65/0.79 % (320924)Peak memory usage: 12 MB
% 2.65/0.79 % (320924)Instructions burned: 9 (million)
% 2.65/0.79 % (320929)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.65/0.79 % (320926)Instruction limit reached!
% 2.65/0.79 % (320926)------------------------------
% 2.65/0.79 % (320926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.79 % (320926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.79 % (320926)CaDiCaL version: 2.1.3
% 2.65/0.79 % (320926)Termination reason: Instruction limit
% 2.65/0.79 % (320926)Termination phase: Saturation
% 2.65/0.79 % (320926)Time elapsed: 0.045 s
% 2.65/0.79 % (320926)Peak memory usage: 13 MB
% 2.65/0.79 % (320926)Instructions burned: 171 (million)
% 2.65/0.79 % (320929)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=803819671:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2996 on theBenchmark for (2996ds/6Mi)
% 2.65/0.79 % (320932)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3287698755:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 2.65/0.79 % (320932)Instruction limit reached!
% 2.65/0.79 % (320932)------------------------------
% 2.65/0.79 % (320932)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.79 % (320932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.79 % (320932)CaDiCaL version: 2.1.3
% 2.65/0.79 % (320932)Termination reason: Instruction limit
% 2.65/0.79 % (320932)Termination phase: Saturation
% 2.65/0.79 % (320932)Time elapsed: 0.006 s
% 2.65/0.79 % (320932)Peak memory usage: 12 MB
% 2.65/0.79 % (320932)Instructions burned: 23 (million)
% 2.65/0.79 % (320929)Instruction limit reached!
% 2.65/0.79 % (320929)------------------------------
% 2.65/0.79 % (320929)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.79 % (320929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.79 % (320929)CaDiCaL version: 2.1.3
% 2.65/0.79 % (320929)Termination reason: Instruction limit
% 2.65/0.79 % (320929)Termination phase: Saturation
% 2.65/0.79 % (320929)Time elapsed: 0.011 s
% 2.65/0.79 % (320929)Peak memory usage: 11 MB
% 2.65/0.79 % (320929)Instructions burned: 6 (million)
% 2.65/0.79 % (320931)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=379932456:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2996 on theBenchmark for (2996ds/22Mi)
% 2.65/0.79 % (320935)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=2187099033:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 2.65/0.79 % (320936)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=1309808431:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 2.65/0.79 % (320918)Instruction limit reached!
% 2.65/0.79 % (320918)------------------------------
% 2.65/0.79 % (320918)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.79 % (320918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.79 % (320918)CaDiCaL version: 2.1.3
% 2.65/0.79 % (320918)Termination reason: Instruction limit
% 2.65/0.79 % (320918)Termination phase: Saturation
% 2.65/0.79 % (320918)Time elapsed: 0.117 s
% 2.65/0.79 % (320918)Peak memory usage: 13 MB
% 2.65/0.79 % (320918)Instructions burned: 195 (million)
% 2.65/0.79 % (320931)Instruction limit reached!
% 2.65/0.79 % (320931)------------------------------
% 2.65/0.79 % (320931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.79 % (320931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.79 % (320931)CaDiCaL version: 2.1.3
% 2.65/0.79 % (320931)Termination reason: Instruction limit
% 2.65/0.79 % (320931)Termination phase: Saturation
% 2.65/0.79 % (320931)Time elapsed: 0.021 s
% 2.65/0.79 % (320931)Peak memory usage: 12 MB
% 2.65/0.79 % (320931)Instructions burned: 23 (million)
% 2.65/0.79 % (320925)Instruction limit reached!
% 2.65/0.79 % (320925)------------------------------
% 2.65/0.79 % (320925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.79 % (320925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.79 % (320925)CaDiCaL version: 2.1.3
% 2.65/0.79 % (320925)Termination reason: Instruction limit
% 2.65/0.79 % (320925)Termination phase: Saturation
% 2.65/0.79 % (320925)Time elapsed: 0.107 s
% 2.65/0.79 % (320925)Peak memory usage: 14 MB
% 2.65/0.79 % (320925)Instructions burned: 183 (million)
% 2.65/0.79 % (320940)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=1882845391:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2995 on theBenchmark for (2995ds/45Mi)
% 2.65/0.79 % (320941)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=2627862591:i=480:rtra=on_2995 on theBenchmark for (2995ds/480Mi)
% 2.65/0.79 % (320891)Instruction limit reached!
% 2.65/0.79 % (320891)------------------------------
% 2.65/0.79 % (320891)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.79 % (320891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.79 % (320891)CaDiCaL version: 2.1.3
% 2.65/0.79 % (320891)Termination reason: Instruction limit
% 2.65/0.79 % (320891)Termination phase: Saturation
% 2.65/0.79 % (320891)Time elapsed: 0.254 s
% 2.65/0.79 % (320891)Peak memory usage: 13 MB
% 2.65/0.79 % (320891)Instructions burned: 327 (million)
% 2.65/0.79 % (320942)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=570377152:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2995 on theBenchmark for (2995ds/21Mi)
% 2.65/0.79 % (320945)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 2.65/0.79 % (320940)Instruction limit reached!
% 2.65/0.79 % (320940)------------------------------
% 2.65/0.79 % (320940)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.79 % (320940)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.79 % (320940)CaDiCaL version: 2.1.3
% 2.65/0.79 % (320940)Termination reason: Instruction limit
% 2.65/0.79 % (320940)Termination phase: Saturation
% 2.65/0.79 % (320940)Time elapsed: 0.042 s
% 2.65/0.79 % (320940)Peak memory usage: 13 MB
% 2.65/0.79 % (320940)Instructions burned: 48 (million)
% 2.65/0.79 % (320942)Instruction limit reached!
% 2.65/0.79 % (320942)------------------------------
% 2.65/0.79 % (320942)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.79 % (320942)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.79 % (320942)CaDiCaL version: 2.1.3
% 2.65/0.79 % (320942)Termination reason: Instruction limit
% 2.65/0.79 % (320942)Termination phase: Saturation
% 2.65/0.79 % (320942)Time elapsed: 0.012 s
% 2.65/0.79 % (320942)Peak memory usage: 12 MB
% 2.65/0.79 % (320942)Instructions burned: 21 (million)
% 2.65/0.79 % (320945)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=1187222052:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/200Mi)
% 2.65/0.79 % (320935)Instruction limit reached!
% 2.65/0.79 % (320935)------------------------------
% 2.65/0.79 % (320935)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.79 % (320935)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.79 % (320935)CaDiCaL version: 2.1.3
% 2.65/0.79 % (320935)Termination reason: Instruction limit
% 2.65/0.79 % (320935)Termination phase: Saturation
% 2.65/0.79 % (320935)Time elapsed: 0.091 s
% 2.65/0.79 % (320935)Peak memory usage: 14 MB
% 2.65/0.79 % (320935)Instructions burned: 317 (million)
% 2.65/0.79 % (320949)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=456753040:i=66:s2at=3:nm=2:rtra=on:rawr=on_2995 on theBenchmark for (2995ds/66Mi)
% 2.65/0.79 % (320947)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=2284963310:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2995 on theBenchmark for (2995ds/13Mi)
% 2.65/0.79 % (320947)Instruction limit reached!
% 2.65/0.79 % (320947)------------------------------
% 2.65/0.79 % (320947)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.79 % (320947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.79 % (320947)CaDiCaL version: 2.1.3
% 2.65/0.79 % (320947)Termination reason: Instruction limit
% 2.65/0.79 % (320947)Termination phase: Saturation
% 2.65/0.79 % (320947)Time elapsed: 0.016 s
% 2.65/0.79 % (320947)Peak memory usage: 12 MB
% 2.65/0.79 % (320947)Instructions burned: 14 (million)
% 2.65/0.79 % (320950)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=2238866523:i=51:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/51Mi)
% 2.65/0.79 % (320949)Instruction limit reached!
% 2.65/0.79 % (320949)------------------------------
% 2.65/0.79 % (320949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.79 % (320949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.79 % (320949)CaDiCaL version: 2.1.3
% 2.65/0.79 % (320949)Termination reason: Instruction limit
% 2.65/0.79 % (320949)Termination phase: Saturation
% 2.65/0.79 % (320949)Time elapsed: 0.035 s
% 2.65/0.79 % (320949)Peak memory usage: 13 MB
% 2.65/0.79 % (320949)Instructions burned: 66 (million)
% 2.65/0.79 % (320953)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=1153581436:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/31Mi)
% 2.65/0.79 % (320945)Instruction limit reached!
% 2.65/0.79 % (320945)------------------------------
% 2.65/0.79 % (320945)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.79 % (320945)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.79 % (320945)CaDiCaL version: 2.1.3
% 2.65/0.79 % (320945)Termination reason: Instruction limit
% 2.65/0.79 % (320945)Termination phase: Saturation
% 2.65/0.79 % (320945)Time elapsed: 0.066 s
% 2.65/0.79 % (320945)Peak memory usage: 13 MB
% 2.65/0.79 % (320945)Instructions burned: 201 (million)
% 2.65/0.79 % (320953)Instruction limit reached!
% 2.65/0.79 % (320953)------------------------------
% 2.65/0.79 % (320953)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.79 % (320953)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.79 % (320953)CaDiCaL version: 2.1.3
% 2.65/0.79 % (320953)Termination reason: Instruction limit
% 2.65/0.79 % (320953)Termination phase: Saturation
% 2.65/0.79 % (320953)Time elapsed: 0.012 s
% 2.65/0.79 % (320953)Peak memory usage: 12 MB
% 2.65/0.79 % (320953)Instructions burned: 35 (million)
% 2.65/0.79 % (320950)Instruction limit reached!
% 2.65/0.79 % (320950)------------------------------
% 2.65/0.79 % (320950)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.79 % (320950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.79 % (320950)CaDiCaL version: 2.1.3
% 2.65/0.79 % (320950)Termination reason: Instruction limit
% 2.65/0.79 % (320950)Termination phase: Saturation
% 2.65/0.79 % (320950)Time elapsed: 0.034 s
% 2.65/0.79 % (320950)Peak memory usage: 12 MB
% 2.65/0.79 % (320950)Instructions burned: 52 (million)
% 2.65/0.79 % (320936) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-320849-320936"...
% 2.65/0.79 % (320957)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=1766572421:cond=on:i=34:hud=10:nm=10:rtra=on_2994 on theBenchmark for (2994ds/34Mi)
% 2.65/0.79 % (320955)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=1520165269:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2994 on theBenchmark for (2994ds/137Mi)
% 2.65/0.79 % (320936)...printing done.
% 2.65/0.79 % (320936)Refutation found. Thanks to Tanya!
% 2.65/0.79 % SZS status Theorem for theBenchmark
% 2.65/0.79 % SZS output start Proof for theBenchmark
% 2.65/0.79 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 2.65/0.79 thf(func_def_0, type, cBIGPHI: ($i > $i)).
% 2.65/0.79 thf(func_def_1, type, cHOM_FROM_HH_1: (($i > $i) > $o)).
% 2.65/0.79 thf(func_def_2, type, cPHI_2: ($i > $i)).
% 2.65/0.79 thf(func_def_3, type, cHOM_FROM_SS_PRIME: (($i > $i) > $o)).
% 2.65/0.79 thf(func_def_4, type, cPHI_1: ($i > $i)).
% 2.65/0.79 thf(func_def_5, type, cSS_PRIME: ($i > $o)).
% 2.65/0.79 thf(func_def_6, type, el1: ($i > ($i > $o) > $o)).
% 2.65/0.79 thf(func_def_7, type, cHH_1: ($i > $o)).
% 2.65/0.79 thf(func_def_8, type, cBIGHI: ($i > $i)).
% 2.65/0.79 thf(func_def_9, type, cHH_2: ($i > $o)).
% 2.65/0.79 thf(func_def_10, type, cTIMES: ($i > $i > $i)).
% 2.65/0.79 thf(func_def_14, type, sK0: (($i > $i) > $i)).
% 2.65/0.79 thf(func_def_15, type, sK1: (($i > $i) > $i)).
% 2.65/0.79 thf(func_def_18, type, sK4: ($i > $i)).
% 2.65/0.79 thf(func_def_19, type, vNOT: ($o > $o)).
% 2.65/0.79 thf(func_def_21, type, db0: !>[X0: $tType]:(X0)).
% 2.65/0.79 thf(func_def_22, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 2.65/0.79 thf(f1,conjecture,(
% 2.65/0.79 ((cHOM_FROM_SS_PRIME @ cPHI_1) & ! [X2 : $i,X1 : $i,X0 : $i,X3 : $i] : (((el1 @ X1 @ cHH_2) & (X2 = X3) & (X0 = X1) & (el1 @ X3 @ cHH_2) & (el1 @ X0 @ cHH_2) & (el1 @ X2 @ cHH_2)) => (((cTIMES @ X0 @ X2)) = ((cTIMES @ X1 @ X3)))) & (! [X5 : $i,X6 : $i] : (((el1 @ X6 @ cHH_1) & (el1 @ X5 @ cHH_1)) => (((cBIGPHI @ (cTIMES @ X5 @ X6))) = ((cTIMES @ (cBIGPHI @ X5) @ (cBIGPHI @ X6))))) <=> (cHOM_FROM_HH_1 @ cBIGPHI)) & ! [X6 : $i,X5 : $i] : (((el1 @ X5 @ cHH_1) & (el1 @ X6 @ cHH_1)) => (el1 @ (cTIMES @ X5 @ X6) @ cHH_1)) & ! [X4 : ($i > $i)] : ((cHOM_FROM_SS_PRIME @ X4) <=> ! [X5 : $i,X6 : $i] : (((el1 @ X5 @ cSS_PRIME) & (el1 @ X6 @ cSS_PRIME)) => (((X4 @ (cTIMES @ X5 @ X6))) = ((cTIMES @ (X4 @ X5) @ (X4 @ X6)))))) & (cHOM_FROM_SS_PRIME @ cPHI_2) & ! [X5 : $i] : ((el1 @ X5 @ cHH_1) => (el1 @ (cBIGPHI @ X5) @ cHH_2)) & ! [X5 : $i] : ((el1 @ X5 @ cSS_PRIME) => (el1 @ (cPHI_2 @ X5) @ cHH_2)) & ! [X0 : $i,X1 : $i,X3 : $i,X2 : $i] : (((el1 @ X1 @ cHH_1) & (X0 = X1) & (X2 = X3) & (el1 @ X0 @ cHH_1) & (el1 @ X2 @ cHH_1) & (el1 @ X3 @ cHH_1)) => (((cTIMES @ X0 @ X2)) = ((cTIMES @ X1 @ X3)))) & ! [X5 : $i] : ((el1 @ X5 @ cSS_PRIME) => (el1 @ (cPHI_1 @ X5) @ cHH_1)) & ! [X5 : $i] : ((el1 @ X5 @ cSS_PRIME) => (((cBIGPHI @ (cPHI_1 @ X5))) = ((cPHI_2 @ X5)))) & ! [X6 : $i] : ((el1 @ X6 @ cHH_1) => ? [X5 : $i] : ((((cPHI_1 @ X5)) = X6) & (el1 @ X5 @ cSS_PRIME))) & ! [X5 : $i,X6 : $i] : (((X5 = X6) & (el1 @ X6 @ cHH_1) & (el1 @ X5 @ cHH_1)) => (((cBIGHI @ X5)) = ((cBIGPHI @ X6)))) & ! [X0 : $i,X1 : $i] : (((el1 @ X1 @ cSS_PRIME) & (el1 @ X0 @ cSS_PRIME)) => (el1 @ (cTIMES @ X0 @ X1) @ cSS_PRIME))) => (cHOM_FROM_HH_1 @ cBIGPHI)),
% 2.65/0.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',cPROB757)).
% 2.65/0.79 thf(f2,negated_conjecture,(
% 2.65/0.79 ~(((cHOM_FROM_SS_PRIME @ cPHI_1) & ! [X2 : $i,X1 : $i,X0 : $i,X3 : $i] : (((el1 @ X1 @ cHH_2) & (X2 = X3) & (X0 = X1) & (el1 @ X3 @ cHH_2) & (el1 @ X0 @ cHH_2) & (el1 @ X2 @ cHH_2)) => (((cTIMES @ X0 @ X2)) = ((cTIMES @ X1 @ X3)))) & (! [X5 : $i,X6 : $i] : (((el1 @ X6 @ cHH_1) & (el1 @ X5 @ cHH_1)) => (((cBIGPHI @ (cTIMES @ X5 @ X6))) = ((cTIMES @ (cBIGPHI @ X5) @ (cBIGPHI @ X6))))) <=> (cHOM_FROM_HH_1 @ cBIGPHI)) & ! [X6 : $i,X5 : $i] : (((el1 @ X5 @ cHH_1) & (el1 @ X6 @ cHH_1)) => (el1 @ (cTIMES @ X5 @ X6) @ cHH_1)) & ! [X4 : ($i > $i)] : ((cHOM_FROM_SS_PRIME @ X4) <=> ! [X5 : $i,X6 : $i] : (((el1 @ X5 @ cSS_PRIME) & (el1 @ X6 @ cSS_PRIME)) => (((X4 @ (cTIMES @ X5 @ X6))) = ((cTIMES @ (X4 @ X5) @ (X4 @ X6)))))) & (cHOM_FROM_SS_PRIME @ cPHI_2) & ! [X5 : $i] : ((el1 @ X5 @ cHH_1) => (el1 @ (cBIGPHI @ X5) @ cHH_2)) & ! [X5 : $i] : ((el1 @ X5 @ cSS_PRIME) => (el1 @ (cPHI_2 @ X5) @ cHH_2)) & ! [X0 : $i,X1 : $i,X3 : $i,X2 : $i] : (((el1 @ X1 @ cHH_1) & (X0 = X1) & (X2 = X3) & (el1 @ X0 @ cHH_1) & (el1 @ X2 @ cHH_1) & (el1 @ X3 @ cHH_1)) => (((cTIMES @ X0 @ X2)) = ((cTIMES @ X1 @ X3)))) & ! [X5 : $i] : ((el1 @ X5 @ cSS_PRIME) => (el1 @ (cPHI_1 @ X5) @ cHH_1)) & ! [X5 : $i] : ((el1 @ X5 @ cSS_PRIME) => (((cBIGPHI @ (cPHI_1 @ X5))) = ((cPHI_2 @ X5)))) & ! [X6 : $i] : ((el1 @ X6 @ cHH_1) => ? [X5 : $i] : ((((cPHI_1 @ X5)) = X6) & (el1 @ X5 @ cSS_PRIME))) & ! [X5 : $i,X6 : $i] : (((X5 = X6) & (el1 @ X6 @ cHH_1) & (el1 @ X5 @ cHH_1)) => (((cBIGHI @ X5)) = ((cBIGPHI @ X6)))) & ! [X0 : $i,X1 : $i] : (((el1 @ X1 @ cSS_PRIME) & (el1 @ X0 @ cSS_PRIME)) => (el1 @ (cTIMES @ X0 @ X1) @ cSS_PRIME))) => (cHOM_FROM_HH_1 @ cBIGPHI))),
% 2.65/0.79 inference(negated_conjecture,[status(cth)],[f1])).
% 2.65/0.79 thf(f3,plain,(
% 2.65/0.79 ~(((cHOM_FROM_SS_PRIME @ cPHI_1) & ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((el1 @ X1 @ cHH_2) & (X0 = X3) & (X1 = X2) & (el1 @ X3 @ cHH_2) & (el1 @ X2 @ cHH_2) & (el1 @ X0 @ cHH_2)) => (((cTIMES @ X1 @ X3)) = ((cTIMES @ X2 @ X0)))) & (! [X4 : $i,X5 : $i] : (((el1 @ X5 @ cHH_1) & (el1 @ X4 @ cHH_1)) => (((cBIGPHI @ (cTIMES @ X4 @ X5))) = ((cTIMES @ (cBIGPHI @ X4) @ (cBIGPHI @ X5))))) <=> (cHOM_FROM_HH_1 @ cBIGPHI)) & ! [X6 : $i,X7 : $i] : (((el1 @ X7 @ cHH_1) & (el1 @ X6 @ cHH_1)) => (el1 @ (cTIMES @ X7 @ X6) @ cHH_1)) & ! [X8 : ($i > $i)] : ((cHOM_FROM_SS_PRIME @ X8) <=> ! [X9 : $i,X10 : $i] : (((el1 @ X9 @ cSS_PRIME) & (el1 @ X10 @ cSS_PRIME)) => (((cTIMES @ (X8 @ X9) @ (X8 @ X10))) = ((X8 @ (cTIMES @ X9 @ X10)))))) & (cHOM_FROM_SS_PRIME @ cPHI_2) & ! [X11 : $i] : ((el1 @ X11 @ cHH_1) => (el1 @ (cBIGPHI @ X11) @ cHH_2)) & ! [X12 : $i] : ((el1 @ X12 @ cSS_PRIME) => (el1 @ (cPHI_2 @ X12) @ cHH_2)) & ! [X13 : $i,X14 : $i,X15 : $i,X16 : $i] : (((el1 @ X14 @ cHH_1) & (X13 = X14) & (X15 = X16) & (el1 @ X13 @ cHH_1) & (el1 @ X16 @ cHH_1) & (el1 @ X15 @ cHH_1)) => (((cTIMES @ X14 @ X15)) = ((cTIMES @ X13 @ X16)))) & ! [X17 : $i] : ((el1 @ X17 @ cSS_PRIME) => (el1 @ (cPHI_1 @ X17) @ cHH_1)) & ! [X18 : $i] : ((el1 @ X18 @ cSS_PRIME) => (((cBIGPHI @ (cPHI_1 @ X18))) = ((cPHI_2 @ X18)))) & ! [X19 : $i] : ((el1 @ X19 @ cHH_1) => ? [X20 : $i] : ((((cPHI_1 @ X20)) = X19) & (el1 @ X20 @ cSS_PRIME))) & ! [X21 : $i,X22 : $i] : (((X21 = X22) & (el1 @ X22 @ cHH_1) & (el1 @ X21 @ cHH_1)) => (((cBIGPHI @ X22)) = ((cBIGHI @ X21)))) & ! [X23 : $i,X24 : $i] : (((el1 @ X24 @ cSS_PRIME) & (el1 @ X23 @ cSS_PRIME)) => (el1 @ (cTIMES @ X23 @ X24) @ cSS_PRIME))) => (cHOM_FROM_HH_1 @ cBIGPHI))),
% 2.65/0.79 inference(rectify,[],[f2])).
% 2.65/0.79 thf(f4,plain,(
% 2.65/0.79 ~((! [X12 : $i] : ((((el1 @ X12 @ cSS_PRIME)) = $true) => ($true = ((el1 @ (cPHI_2 @ X12) @ cHH_2)))) & ! [X8 : ($i > $i)] : (! [X9 : $i,X10 : $i] : ((($true = ((el1 @ X10 @ cSS_PRIME))) & ($true = ((el1 @ X9 @ cSS_PRIME)))) => (((cTIMES @ (X8 @ X9) @ (X8 @ X10))) = ((X8 @ (cTIMES @ X9 @ X10))))) <=> (((cHOM_FROM_SS_PRIME @ X8)) = $true)) & ! [X11 : $i] : ((((el1 @ X11 @ cHH_1)) = $true) => ($true = ((el1 @ (cBIGPHI @ X11) @ cHH_2)))) & ! [X18 : $i] : (($true = ((el1 @ X18 @ cSS_PRIME))) => (((cBIGPHI @ (cPHI_1 @ X18))) = ((cPHI_2 @ X18)))) & ! [X17 : $i] : (($true = ((el1 @ X17 @ cSS_PRIME))) => (((el1 @ (cPHI_1 @ X17) @ cHH_1)) = $true)) & ! [X13 : $i,X16 : $i,X15 : $i,X14 : $i] : (((X15 = X16) & ($true = ((el1 @ X15 @ cHH_1))) & (X13 = X14) & ($true = ((el1 @ X13 @ cHH_1))) & (((el1 @ X16 @ cHH_1)) = $true) & ($true = ((el1 @ X14 @ cHH_1)))) => (((cTIMES @ X14 @ X15)) = ((cTIMES @ X13 @ X16)))) & ! [X23 : $i,X24 : $i] : ((($true = ((el1 @ X24 @ cSS_PRIME))) & ($true = ((el1 @ X23 @ cSS_PRIME)))) => ($true = ((el1 @ (cTIMES @ X23 @ X24) @ cSS_PRIME)))) & ((((cHOM_FROM_HH_1 @ cBIGPHI)) = $true) <=> ! [X4 : $i,X5 : $i] : (((((el1 @ X5 @ cHH_1)) = $true) & ($true = ((el1 @ X4 @ cHH_1)))) => (((cBIGPHI @ (cTIMES @ X4 @ X5))) = ((cTIMES @ (cBIGPHI @ X4) @ (cBIGPHI @ X5)))))) & ! [X7 : $i,X6 : $i] : (((((el1 @ X6 @ cHH_1)) = $true) & ($true = ((el1 @ X7 @ cHH_1)))) => ($true = ((el1 @ (cTIMES @ X7 @ X6) @ cHH_1)))) & (((cHOM_FROM_SS_PRIME @ cPHI_2)) = $true) & ! [X22 : $i,X21 : $i] : ((($true = ((el1 @ X21 @ cHH_1))) & (X21 = X22) & ($true = ((el1 @ X22 @ cHH_1)))) => (((cBIGPHI @ X22)) = ((cBIGHI @ X21)))) & ! [X3 : $i,X1 : $i,X2 : $i,X0 : $i] : (((((el1 @ X0 @ cHH_2)) = $true) & (((el1 @ X3 @ cHH_2)) = $true) & (((el1 @ X1 @ cHH_2)) = $true) & (((el1 @ X2 @ cHH_2)) = $true) & (X1 = X2) & (X0 = X3)) => (((cTIMES @ X1 @ X3)) = ((cTIMES @ X2 @ X0)))) & (((cHOM_FROM_SS_PRIME @ cPHI_1)) = $true) & ! [X19 : $i] : (($true = ((el1 @ X19 @ cHH_1))) => ? [X20 : $i] : ((((cPHI_1 @ X20)) = X19) & ($true = ((el1 @ X20 @ cSS_PRIME)))))) => (((cHOM_FROM_HH_1 @ cBIGPHI)) = $true))),
% 2.65/0.79 inference(fool_elimination,[],[f3])).
% 2.65/0.79 thf(f5,plain,(
% 2.65/0.79 (((cHOM_FROM_HH_1 @ cBIGPHI)) != $true) & (! [X12 : $i] : (($true = ((el1 @ (cPHI_2 @ X12) @ cHH_2))) | (((el1 @ X12 @ cSS_PRIME)) != $true)) & ! [X8 : ($i > $i)] : (! [X9 : $i,X10 : $i] : ((((cTIMES @ (X8 @ X9) @ (X8 @ X10))) = ((X8 @ (cTIMES @ X9 @ X10)))) | (($true != ((el1 @ X10 @ cSS_PRIME))) | ($true != ((el1 @ X9 @ cSS_PRIME))))) <=> (((cHOM_FROM_SS_PRIME @ X8)) = $true)) & ! [X11 : $i] : (($true = ((el1 @ (cBIGPHI @ X11) @ cHH_2))) | (((el1 @ X11 @ cHH_1)) != $true)) & ! [X18 : $i] : ((((cBIGPHI @ (cPHI_1 @ X18))) = ((cPHI_2 @ X18))) | ($true != ((el1 @ X18 @ cSS_PRIME)))) & ! [X17 : $i] : ((((el1 @ (cPHI_1 @ X17) @ cHH_1)) = $true) | ($true != ((el1 @ X17 @ cSS_PRIME)))) & ! [X13 : $i,X16 : $i,X15 : $i,X14 : $i] : ((((cTIMES @ X14 @ X15)) = ((cTIMES @ X13 @ X16))) | ((X15 != X16) | ($true != ((el1 @ X15 @ cHH_1))) | (X13 != X14) | ($true != ((el1 @ X13 @ cHH_1))) | (((el1 @ X16 @ cHH_1)) != $true) | ($true != ((el1 @ X14 @ cHH_1))))) & ! [X23 : $i,X24 : $i] : (($true = ((el1 @ (cTIMES @ X23 @ X24) @ cSS_PRIME))) | (($true != ((el1 @ X24 @ cSS_PRIME))) | ($true != ((el1 @ X23 @ cSS_PRIME))))) & ((((cHOM_FROM_HH_1 @ cBIGPHI)) = $true) <=> ! [X4 : $i,X5 : $i] : ((((cBIGPHI @ (cTIMES @ X4 @ X5))) = ((cTIMES @ (cBIGPHI @ X4) @ (cBIGPHI @ X5)))) | ((((el1 @ X5 @ cHH_1)) != $true) | ($true != ((el1 @ X4 @ cHH_1)))))) & ! [X7 : $i,X6 : $i] : (($true = ((el1 @ (cTIMES @ X7 @ X6) @ cHH_1))) | ((((el1 @ X6 @ cHH_1)) != $true) | ($true != ((el1 @ X7 @ cHH_1))))) & (((cHOM_FROM_SS_PRIME @ cPHI_2)) = $true) & ! [X22 : $i,X21 : $i] : ((((cBIGPHI @ X22)) = ((cBIGHI @ X21))) | (($true != ((el1 @ X21 @ cHH_1))) | (X21 != X22) | ($true != ((el1 @ X22 @ cHH_1))))) & ! [X3 : $i,X1 : $i,X2 : $i,X0 : $i] : ((((cTIMES @ X1 @ X3)) = ((cTIMES @ X2 @ X0))) | ((((el1 @ X0 @ cHH_2)) != $true) | (((el1 @ X3 @ cHH_2)) != $true) | (((el1 @ X1 @ cHH_2)) != $true) | (((el1 @ X2 @ cHH_2)) != $true) | (X1 != X2) | (X0 != X3))) & (((cHOM_FROM_SS_PRIME @ cPHI_1)) = $true) & ! [X19 : $i] : (? [X20 : $i] : ((((cPHI_1 @ X20)) = X19) & ($true = ((el1 @ X20 @ cSS_PRIME)))) | ($true != ((el1 @ X19 @ cHH_1)))))),
% 2.65/0.79 inference(ennf_transformation,[],[f4])).
% 2.65/0.79 thf(f6,plain,(
% 2.65/0.79 ! [X11 : $i] : (($true = ((el1 @ (cBIGPHI @ X11) @ cHH_2))) | (((el1 @ X11 @ cHH_1)) != $true)) & ! [X8 : ($i > $i)] : ((((cHOM_FROM_SS_PRIME @ X8)) = $true) <=> ! [X10 : $i,X9 : $i] : (($true != ((el1 @ X10 @ cSS_PRIME))) | ($true != ((el1 @ X9 @ cSS_PRIME))) | (((cTIMES @ (X8 @ X9) @ (X8 @ X10))) = ((X8 @ (cTIMES @ X9 @ X10)))))) & (((cHOM_FROM_SS_PRIME @ cPHI_2)) = $true) & ! [X2 : $i,X1 : $i,X3 : $i,X0 : $i] : ((((cTIMES @ X1 @ X3)) = ((cTIMES @ X2 @ X0))) | (X0 != X3) | (((el1 @ X2 @ cHH_2)) != $true) | (((el1 @ X0 @ cHH_2)) != $true) | (((el1 @ X3 @ cHH_2)) != $true) | (((el1 @ X1 @ cHH_2)) != $true) | (X1 != X2)) & ((((cHOM_FROM_HH_1 @ cBIGPHI)) = $true) <=> ! [X5 : $i,X4 : $i] : ((((cBIGPHI @ (cTIMES @ X4 @ X5))) = ((cTIMES @ (cBIGPHI @ X4) @ (cBIGPHI @ X5)))) | ($true != ((el1 @ X4 @ cHH_1))) | (((el1 @ X5 @ cHH_1)) != $true))) & ! [X23 : $i,X24 : $i] : (($true = ((el1 @ (cTIMES @ X23 @ X24) @ cSS_PRIME))) | ($true != ((el1 @ X24 @ cSS_PRIME))) | ($true != ((el1 @ X23 @ cSS_PRIME)))) & ! [X22 : $i,X21 : $i] : (($true != ((el1 @ X21 @ cHH_1))) | (((cBIGPHI @ X22)) = ((cBIGHI @ X21))) | ($true != ((el1 @ X22 @ cHH_1))) | (X21 != X22)) & ! [X18 : $i] : ((((cBIGPHI @ (cPHI_1 @ X18))) = ((cPHI_2 @ X18))) | ($true != ((el1 @ X18 @ cSS_PRIME)))) & ! [X13 : $i,X16 : $i,X14 : $i,X15 : $i] : (($true != ((el1 @ X13 @ cHH_1))) | ($true != ((el1 @ X15 @ cHH_1))) | (((el1 @ X16 @ cHH_1)) != $true) | (X13 != X14) | (X15 != X16) | ($true != ((el1 @ X14 @ cHH_1))) | (((cTIMES @ X14 @ X15)) = ((cTIMES @ X13 @ X16)))) & ! [X19 : $i] : (? [X20 : $i] : ((((cPHI_1 @ X20)) = X19) & ($true = ((el1 @ X20 @ cSS_PRIME)))) | ($true != ((el1 @ X19 @ cHH_1)))) & ! [X6 : $i,X7 : $i] : (($true != ((el1 @ X7 @ cHH_1))) | ($true = ((el1 @ (cTIMES @ X7 @ X6) @ cHH_1))) | (((el1 @ X6 @ cHH_1)) != $true)) & (((cHOM_FROM_SS_PRIME @ cPHI_1)) = $true) & ! [X17 : $i] : ((((el1 @ (cPHI_1 @ X17) @ cHH_1)) = $true) | ($true != ((el1 @ X17 @ cSS_PRIME)))) & (((cHOM_FROM_HH_1 @ cBIGPHI)) != $true) & ! [X12 : $i] : (($true = ((el1 @ (cPHI_2 @ X12) @ cHH_2))) | (((el1 @ X12 @ cSS_PRIME)) != $true))),
% 2.65/0.79 inference(flattening,[],[f5])).
% 2.65/0.79 thf(f7,plain,(
% 2.65/0.79 ! [X11 : $i] : (($true = ((el1 @ (cBIGPHI @ X11) @ cHH_2))) | (((el1 @ X11 @ cHH_1)) != $true)) & ! [X8 : ($i > $i)] : (((((cHOM_FROM_SS_PRIME @ X8)) = $true) | ? [X10 : $i,X9 : $i] : (($true = ((el1 @ X10 @ cSS_PRIME))) & ($true = ((el1 @ X9 @ cSS_PRIME))) & (((cTIMES @ (X8 @ X9) @ (X8 @ X10))) != ((X8 @ (cTIMES @ X9 @ X10)))))) & (! [X10 : $i,X9 : $i] : (($true != ((el1 @ X10 @ cSS_PRIME))) | ($true != ((el1 @ X9 @ cSS_PRIME))) | (((cTIMES @ (X8 @ X9) @ (X8 @ X10))) = ((X8 @ (cTIMES @ X9 @ X10))))) | (((cHOM_FROM_SS_PRIME @ X8)) != $true))) & (((cHOM_FROM_SS_PRIME @ cPHI_2)) = $true) & ! [X2 : $i,X1 : $i,X3 : $i,X0 : $i] : ((((cTIMES @ X1 @ X3)) = ((cTIMES @ X2 @ X0))) | (X0 != X3) | (((el1 @ X2 @ cHH_2)) != $true) | (((el1 @ X0 @ cHH_2)) != $true) | (((el1 @ X3 @ cHH_2)) != $true) | (((el1 @ X1 @ cHH_2)) != $true) | (X1 != X2)) & (((((cHOM_FROM_HH_1 @ cBIGPHI)) = $true) | ? [X5 : $i,X4 : $i] : ((((cBIGPHI @ (cTIMES @ X4 @ X5))) != ((cTIMES @ (cBIGPHI @ X4) @ (cBIGPHI @ X5)))) & ($true = ((el1 @ X4 @ cHH_1))) & (((el1 @ X5 @ cHH_1)) = $true))) & (! [X5 : $i,X4 : $i] : ((((cBIGPHI @ (cTIMES @ X4 @ X5))) = ((cTIMES @ (cBIGPHI @ X4) @ (cBIGPHI @ X5)))) | ($true != ((el1 @ X4 @ cHH_1))) | (((el1 @ X5 @ cHH_1)) != $true)) | (((cHOM_FROM_HH_1 @ cBIGPHI)) != $true))) & ! [X23 : $i,X24 : $i] : (($true = ((el1 @ (cTIMES @ X23 @ X24) @ cSS_PRIME))) | ($true != ((el1 @ X24 @ cSS_PRIME))) | ($true != ((el1 @ X23 @ cSS_PRIME)))) & ! [X22 : $i,X21 : $i] : (($true != ((el1 @ X21 @ cHH_1))) | (((cBIGPHI @ X22)) = ((cBIGHI @ X21))) | ($true != ((el1 @ X22 @ cHH_1))) | (X21 != X22)) & ! [X18 : $i] : ((((cBIGPHI @ (cPHI_1 @ X18))) = ((cPHI_2 @ X18))) | ($true != ((el1 @ X18 @ cSS_PRIME)))) & ! [X13 : $i,X16 : $i,X14 : $i,X15 : $i] : (($true != ((el1 @ X13 @ cHH_1))) | ($true != ((el1 @ X15 @ cHH_1))) | (((el1 @ X16 @ cHH_1)) != $true) | (X13 != X14) | (X15 != X16) | ($true != ((el1 @ X14 @ cHH_1))) | (((cTIMES @ X14 @ X15)) = ((cTIMES @ X13 @ X16)))) & ! [X19 : $i] : (? [X20 : $i] : ((((cPHI_1 @ X20)) = X19) & ($true = ((el1 @ X20 @ cSS_PRIME)))) | ($true != ((el1 @ X19 @ cHH_1)))) & ! [X6 : $i,X7 : $i] : (($true != ((el1 @ X7 @ cHH_1))) | ($true = ((el1 @ (cTIMES @ X7 @ X6) @ cHH_1))) | (((el1 @ X6 @ cHH_1)) != $true)) & (((cHOM_FROM_SS_PRIME @ cPHI_1)) = $true) & ! [X17 : $i] : ((((el1 @ (cPHI_1 @ X17) @ cHH_1)) = $true) | ($true != ((el1 @ X17 @ cSS_PRIME)))) & (((cHOM_FROM_HH_1 @ cBIGPHI)) != $true) & ! [X12 : $i] : (($true = ((el1 @ (cPHI_2 @ X12) @ cHH_2))) | (((el1 @ X12 @ cSS_PRIME)) != $true))),
% 2.65/0.79 inference(nnf_transformation,[],[f6])).
% 2.65/0.79 thf(f8,plain,(
% 2.65/0.79 ! [X11 : $i] : (($true = ((el1 @ (cBIGPHI @ X11) @ cHH_2))) | (((el1 @ X11 @ cHH_1)) != $true)) & ! [X8 : ($i > $i)] : (((((cHOM_FROM_SS_PRIME @ X8)) = $true) | ? [X10 : $i,X9 : $i] : (($true = ((el1 @ X10 @ cSS_PRIME))) & ($true = ((el1 @ X9 @ cSS_PRIME))) & (((cTIMES @ (X8 @ X9) @ (X8 @ X10))) != ((X8 @ (cTIMES @ X9 @ X10)))))) & (! [X10 : $i,X9 : $i] : (($true != ((el1 @ X10 @ cSS_PRIME))) | ($true != ((el1 @ X9 @ cSS_PRIME))) | (((cTIMES @ (X8 @ X9) @ (X8 @ X10))) = ((X8 @ (cTIMES @ X9 @ X10))))) | (((cHOM_FROM_SS_PRIME @ X8)) != $true))) & (((cHOM_FROM_SS_PRIME @ cPHI_2)) = $true) & ! [X2 : $i,X1 : $i,X3 : $i,X0 : $i] : ((((cTIMES @ X1 @ X3)) = ((cTIMES @ X2 @ X0))) | (X0 != X3) | (((el1 @ X2 @ cHH_2)) != $true) | (((el1 @ X0 @ cHH_2)) != $true) | (((el1 @ X3 @ cHH_2)) != $true) | (((el1 @ X1 @ cHH_2)) != $true) | (X1 != X2)) & ((((cHOM_FROM_HH_1 @ cBIGPHI)) = $true) | ? [X5 : $i,X4 : $i] : ((((cBIGPHI @ (cTIMES @ X4 @ X5))) != ((cTIMES @ (cBIGPHI @ X4) @ (cBIGPHI @ X5)))) & ($true = ((el1 @ X4 @ cHH_1))) & (((el1 @ X5 @ cHH_1)) = $true))) & (! [X5 : $i,X4 : $i] : ((((cBIGPHI @ (cTIMES @ X4 @ X5))) = ((cTIMES @ (cBIGPHI @ X4) @ (cBIGPHI @ X5)))) | ($true != ((el1 @ X4 @ cHH_1))) | (((el1 @ X5 @ cHH_1)) != $true)) | (((cHOM_FROM_HH_1 @ cBIGPHI)) != $true)) & ! [X23 : $i,X24 : $i] : (($true = ((el1 @ (cTIMES @ X23 @ X24) @ cSS_PRIME))) | ($true != ((el1 @ X24 @ cSS_PRIME))) | ($true != ((el1 @ X23 @ cSS_PRIME)))) & ! [X22 : $i,X21 : $i] : (($true != ((el1 @ X21 @ cHH_1))) | (((cBIGPHI @ X22)) = ((cBIGHI @ X21))) | ($true != ((el1 @ X22 @ cHH_1))) | (X21 != X22)) & ! [X18 : $i] : ((((cBIGPHI @ (cPHI_1 @ X18))) = ((cPHI_2 @ X18))) | ($true != ((el1 @ X18 @ cSS_PRIME)))) & ! [X13 : $i,X16 : $i,X14 : $i,X15 : $i] : (($true != ((el1 @ X13 @ cHH_1))) | ($true != ((el1 @ X15 @ cHH_1))) | (((el1 @ X16 @ cHH_1)) != $true) | (X13 != X14) | (X15 != X16) | ($true != ((el1 @ X14 @ cHH_1))) | (((cTIMES @ X14 @ X15)) = ((cTIMES @ X13 @ X16)))) & ! [X19 : $i] : (? [X20 : $i] : ((((cPHI_1 @ X20)) = X19) & ($true = ((el1 @ X20 @ cSS_PRIME)))) | ($true != ((el1 @ X19 @ cHH_1)))) & ! [X6 : $i,X7 : $i] : (($true != ((el1 @ X7 @ cHH_1))) | ($true = ((el1 @ (cTIMES @ X7 @ X6) @ cHH_1))) | (((el1 @ X6 @ cHH_1)) != $true)) & (((cHOM_FROM_SS_PRIME @ cPHI_1)) = $true) & ! [X17 : $i] : ((((el1 @ (cPHI_1 @ X17) @ cHH_1)) = $true) | ($true != ((el1 @ X17 @ cSS_PRIME)))) & (((cHOM_FROM_HH_1 @ cBIGPHI)) != $true) & ! [X12 : $i] : (($true = ((el1 @ (cPHI_2 @ X12) @ cHH_2))) | (((el1 @ X12 @ cSS_PRIME)) != $true))),
% 2.65/0.79 inference(flattening,[],[f7])).
% 2.65/0.79 thf(f9,plain,(
% 2.65/0.79 ! [X0 : $i] : (($true = ((el1 @ (cBIGPHI @ X0) @ cHH_2))) | (((el1 @ X0 @ cHH_1)) != $true)) & ! [X1 : ($i > $i)] : ((($true = ((cHOM_FROM_SS_PRIME @ X1))) | ? [X2 : $i,X3 : $i] : (($true = ((el1 @ X2 @ cSS_PRIME))) & ($true = ((el1 @ X3 @ cSS_PRIME))) & (((cTIMES @ (X1 @ X3) @ (X1 @ X2))) != ((X1 @ (cTIMES @ X3 @ X2)))))) & (! [X4 : $i,X5 : $i] : (($true != ((el1 @ X4 @ cSS_PRIME))) | (((el1 @ X5 @ cSS_PRIME)) != $true) | (((cTIMES @ (X1 @ X5) @ (X1 @ X4))) = ((X1 @ (cTIMES @ X5 @ X4))))) | ($true != ((cHOM_FROM_SS_PRIME @ X1))))) & (((cHOM_FROM_SS_PRIME @ cPHI_2)) = $true) & ! [X6 : $i,X7 : $i,X8 : $i,X9 : $i] : ((((cTIMES @ X7 @ X8)) = ((cTIMES @ X6 @ X9))) | (X8 != X9) | ($true != ((el1 @ X6 @ cHH_2))) | ($true != ((el1 @ X9 @ cHH_2))) | (((el1 @ X8 @ cHH_2)) != $true) | ($true != ((el1 @ X7 @ cHH_2))) | (X6 != X7)) & ((((cHOM_FROM_HH_1 @ cBIGPHI)) = $true) | ? [X10 : $i,X11 : $i] : ((((cTIMES @ (cBIGPHI @ X11) @ (cBIGPHI @ X10))) != ((cBIGPHI @ (cTIMES @ X11 @ X10)))) & (((el1 @ X11 @ cHH_1)) = $true) & ($true = ((el1 @ X10 @ cHH_1))))) & (! [X12 : $i,X13 : $i] : ((((cBIGPHI @ (cTIMES @ X13 @ X12))) = ((cTIMES @ (cBIGPHI @ X13) @ (cBIGPHI @ X12)))) | ($true != ((el1 @ X13 @ cHH_1))) | (((el1 @ X12 @ cHH_1)) != $true)) | (((cHOM_FROM_HH_1 @ cBIGPHI)) != $true)) & ! [X14 : $i,X15 : $i] : (($true = ((el1 @ (cTIMES @ X14 @ X15) @ cSS_PRIME))) | ($true != ((el1 @ X15 @ cSS_PRIME))) | ($true != ((el1 @ X14 @ cSS_PRIME)))) & ! [X16 : $i,X17 : $i] : (($true != ((el1 @ X17 @ cHH_1))) | (((cBIGPHI @ X16)) = ((cBIGHI @ X17))) | (((el1 @ X16 @ cHH_1)) != $true) | (X16 != X17)) & ! [X18 : $i] : ((((cBIGPHI @ (cPHI_1 @ X18))) = ((cPHI_2 @ X18))) | ($true != ((el1 @ X18 @ cSS_PRIME)))) & ! [X19 : $i,X20 : $i,X21 : $i,X22 : $i] : (($true != ((el1 @ X19 @ cHH_1))) | ($true != ((el1 @ X22 @ cHH_1))) | ($true != ((el1 @ X20 @ cHH_1))) | (X19 != X21) | (X20 != X22) | ($true != ((el1 @ X21 @ cHH_1))) | (((cTIMES @ X19 @ X20)) = ((cTIMES @ X21 @ X22)))) & ! [X23 : $i] : (? [X24 : $i] : ((((cPHI_1 @ X24)) = X23) & ($true = ((el1 @ X24 @ cSS_PRIME)))) | ($true != ((el1 @ X23 @ cHH_1)))) & ! [X25 : $i,X26 : $i] : (($true != ((el1 @ X26 @ cHH_1))) | ($true = ((el1 @ (cTIMES @ X26 @ X25) @ cHH_1))) | ($true != ((el1 @ X25 @ cHH_1)))) & (((cHOM_FROM_SS_PRIME @ cPHI_1)) = $true) & ! [X27 : $i] : (($true = ((el1 @ (cPHI_1 @ X27) @ cHH_1))) | ($true != ((el1 @ X27 @ cSS_PRIME)))) & (((cHOM_FROM_HH_1 @ cBIGPHI)) != $true) & ! [X28 : $i] : (($true = ((el1 @ (cPHI_2 @ X28) @ cHH_2))) | ($true != ((el1 @ X28 @ cSS_PRIME))))),
% 2.65/0.79 inference(rectify,[],[f8])).
% 2.65/0.79 thf(f10,plain,(
% 2.65/0.79 ! [X0 : $i] : (($true = ((el1 @ (cBIGPHI @ X0) @ cHH_2))) | (((el1 @ X0 @ cHH_1)) != $true)) & ! [X1 : ($i > $i)] : ((($true = ((cHOM_FROM_SS_PRIME @ X1))) | (($true = ((el1 @ (sK0 @ X1) @ cSS_PRIME))) & ($true = ((el1 @ (sK1 @ X1) @ cSS_PRIME))) & (((X1 @ (cTIMES @ (sK1 @ X1) @ (sK0 @ X1)))) != ((cTIMES @ (X1 @ (sK1 @ X1)) @ (X1 @ (sK0 @ X1))))))) & (! [X4 : $i,X5 : $i] : (($true != ((el1 @ X4 @ cSS_PRIME))) | (((el1 @ X5 @ cSS_PRIME)) != $true) | (((cTIMES @ (X1 @ X5) @ (X1 @ X4))) = ((X1 @ (cTIMES @ X5 @ X4))))) | ($true != ((cHOM_FROM_SS_PRIME @ X1))))) & (((cHOM_FROM_SS_PRIME @ cPHI_2)) = $true) & ! [X6 : $i,X7 : $i,X8 : $i,X9 : $i] : ((((cTIMES @ X7 @ X8)) = ((cTIMES @ X6 @ X9))) | (X8 != X9) | ($true != ((el1 @ X6 @ cHH_2))) | ($true != ((el1 @ X9 @ cHH_2))) | (((el1 @ X8 @ cHH_2)) != $true) | ($true != ((el1 @ X7 @ cHH_2))) | (X6 != X7)) & ((((cHOM_FROM_HH_1 @ cBIGPHI)) = $true) | ((((cTIMES @ (cBIGPHI @ sK3) @ (cBIGPHI @ sK2))) != ((cBIGPHI @ (cTIMES @ sK3 @ sK2)))) & (((el1 @ sK3 @ cHH_1)) = $true) & ($true = ((el1 @ sK2 @ cHH_1))))) & (! [X12 : $i,X13 : $i] : ((((cBIGPHI @ (cTIMES @ X13 @ X12))) = ((cTIMES @ (cBIGPHI @ X13) @ (cBIGPHI @ X12)))) | ($true != ((el1 @ X13 @ cHH_1))) | (((el1 @ X12 @ cHH_1)) != $true)) | (((cHOM_FROM_HH_1 @ cBIGPHI)) != $true)) & ! [X14 : $i,X15 : $i] : (($true = ((el1 @ (cTIMES @ X14 @ X15) @ cSS_PRIME))) | ($true != ((el1 @ X15 @ cSS_PRIME))) | ($true != ((el1 @ X14 @ cSS_PRIME)))) & ! [X16 : $i,X17 : $i] : (($true != ((el1 @ X17 @ cHH_1))) | (((cBIGPHI @ X16)) = ((cBIGHI @ X17))) | (((el1 @ X16 @ cHH_1)) != $true) | (X16 != X17)) & ! [X18 : $i] : ((((cBIGPHI @ (cPHI_1 @ X18))) = ((cPHI_2 @ X18))) | ($true != ((el1 @ X18 @ cSS_PRIME)))) & ! [X19 : $i,X20 : $i,X21 : $i,X22 : $i] : (($true != ((el1 @ X19 @ cHH_1))) | ($true != ((el1 @ X22 @ cHH_1))) | ($true != ((el1 @ X20 @ cHH_1))) | (X19 != X21) | (X20 != X22) | ($true != ((el1 @ X21 @ cHH_1))) | (((cTIMES @ X19 @ X20)) = ((cTIMES @ X21 @ X22)))) & ! [X23 : $i] : (((((cPHI_1 @ (sK4 @ X23))) = X23) & ($true = ((el1 @ (sK4 @ X23) @ cSS_PRIME)))) | ($true != ((el1 @ X23 @ cHH_1)))) & ! [X25 : $i,X26 : $i] : (($true != ((el1 @ X26 @ cHH_1))) | ($true = ((el1 @ (cTIMES @ X26 @ X25) @ cHH_1))) | ($true != ((el1 @ X25 @ cHH_1)))) & (((cHOM_FROM_SS_PRIME @ cPHI_1)) = $true) & ! [X27 : $i] : (($true = ((el1 @ (cPHI_1 @ X27) @ cHH_1))) | ($true != ((el1 @ X27 @ cSS_PRIME)))) & (((cHOM_FROM_HH_1 @ cBIGPHI)) != $true) & ! [X28 : $i] : (($true = ((el1 @ (cPHI_2 @ X28) @ cHH_2))) | ($true != ((el1 @ X28 @ cSS_PRIME))))),
% 2.65/0.79 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,vAPP,sK2,sK3,vAPP]),skolemize(X24,sK4 @ X23),skolemize(X24,sK4 @ X23),skolemize(X10,sK2),skolemize(X11,sK3),skolemize(X24,sK4 @ X23)],[f9])).
% 2.65/0.79 thf(f12,plain,(
% 2.65/0.79 (((cHOM_FROM_HH_1 @ cBIGPHI)) != $true)),
% 2.65/0.79 inference(cnf_transformation,[],[f10])).
% 2.65/0.79 thf(f14,plain,(
% 2.65/0.79 (((cHOM_FROM_SS_PRIME @ cPHI_1)) = $true)),
% 2.65/0.79 inference(cnf_transformation,[],[f10])).
% 2.65/0.79 thf(f15,plain,(
% 2.65/0.79 ( ! [X26 : $i,X25 : $i] : (($true != ((el1 @ X26 @ cHH_1))) | ($true != ((el1 @ X25 @ cHH_1))) | ($true = ((el1 @ (cTIMES @ X26 @ X25) @ cHH_1)))) )),
% 2.65/0.79 inference(cnf_transformation,[],[f10])).
% 2.65/0.79 thf(f16,plain,(
% 2.65/0.79 ( ! [X23 : $i] : (($true != ((el1 @ X23 @ cHH_1))) | ($true = ((el1 @ (sK4 @ X23) @ cSS_PRIME)))) )),
% 2.65/0.79 inference(cnf_transformation,[],[f10])).
% 2.65/0.79 thf(f17,plain,(
% 2.65/0.79 ( ! [X23 : $i] : (($true != ((el1 @ X23 @ cHH_1))) | (((cPHI_1 @ (sK4 @ X23))) = X23)) )),
% 2.65/0.79 inference(cnf_transformation,[],[f10])).
% 2.65/0.79 thf(f19,plain,(
% 2.65/0.79 ( ! [X18 : $i] : (($true != ((el1 @ X18 @ cSS_PRIME))) | (((cBIGPHI @ (cPHI_1 @ X18))) = ((cPHI_2 @ X18)))) )),
% 2.65/0.79 inference(cnf_transformation,[],[f10])).
% 2.65/0.79 thf(f20,plain,(
% 2.65/0.79 ( ! [X16 : $i,X17 : $i] : (($true != ((el1 @ X17 @ cHH_1))) | (((cBIGPHI @ X16)) = ((cBIGHI @ X17))) | (((el1 @ X16 @ cHH_1)) != $true) | (X16 != X17)) )),
% 2.65/0.79 inference(cnf_transformation,[],[f10])).
% 2.65/0.79 thf(f21,plain,(
% 2.65/0.79 ( ! [X14 : $i,X15 : $i] : (($true != ((el1 @ X15 @ cSS_PRIME))) | ($true = ((el1 @ (cTIMES @ X14 @ X15) @ cSS_PRIME))) | ($true != ((el1 @ X14 @ cSS_PRIME)))) )),
% 2.65/0.79 inference(cnf_transformation,[],[f10])).
% 2.65/0.79 thf(f23,plain,(
% 2.65/0.79 ($true = ((el1 @ sK2 @ cHH_1))) | (((cHOM_FROM_HH_1 @ cBIGPHI)) = $true)),
% 2.65/0.79 inference(cnf_transformation,[],[f10])).
% 2.65/0.79 thf(f24,plain,(
% 2.65/0.79 (((cHOM_FROM_HH_1 @ cBIGPHI)) = $true) | (((el1 @ sK3 @ cHH_1)) = $true)),
% 2.65/0.79 inference(cnf_transformation,[],[f10])).
% 2.65/0.79 thf(f25,plain,(
% 2.65/0.79 (((cHOM_FROM_HH_1 @ cBIGPHI)) = $true) | (((cTIMES @ (cBIGPHI @ sK3) @ (cBIGPHI @ sK2))) != ((cBIGPHI @ (cTIMES @ sK3 @ sK2))))),
% 2.65/0.79 inference(cnf_transformation,[],[f10])).
% 2.65/0.79 thf(f27,plain,(
% 2.65/0.79 (((cHOM_FROM_SS_PRIME @ cPHI_2)) = $true)),
% 2.65/0.79 inference(cnf_transformation,[],[f10])).
% 2.65/0.79 thf(f28,plain,(
% 2.65/0.79 ( ! [X1 : ($i > $i),X4 : $i,X5 : $i] : (($true != ((el1 @ X4 @ cSS_PRIME))) | (((el1 @ X5 @ cSS_PRIME)) != $true) | ($true != ((cHOM_FROM_SS_PRIME @ X1))) | (((cTIMES @ (X1 @ X5) @ (X1 @ X4))) = ((X1 @ (cTIMES @ X5 @ X4))))) )),
% 2.65/0.79 inference(cnf_transformation,[],[f10])).
% 2.65/0.79 thf(f37,plain,(
% 2.65/0.79 ( ! [X17 : $i] : ((((cBIGHI @ X17)) = ((cBIGPHI @ X17))) | ($true != ((el1 @ X17 @ cHH_1))) | ($true != ((el1 @ X17 @ cHH_1)))) )),
% 2.65/0.79 inference(equality_resolution,[],[f20])).
% 2.65/0.79 thf(f40,plain,(
% 2.65/0.79 ( ! [X17 : $i] : (($true != ((el1 @ X17 @ cHH_1))) | (((cBIGHI @ X17)) = ((cBIGPHI @ X17)))) )),
% 2.65/0.79 inference(duplicate_literal_removal,[],[f37])).
% 2.65/0.79 thf(f44,definition,(
% 2.65/0.79 spl5_1 <=> (((cHOM_FROM_HH_1 @ cBIGPHI)) = $true)),
% 2.65/0.79 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 2.65/0.79 thf(f47,plain,(
% 2.65/0.79 ~spl5_1),
% 2.65/0.79 inference(avatar_split_clause,[],[f12,f44])).
% 2.65/0.79 thf(f49,definition,(
% 2.65/0.79 spl5_2 <=> (((el1 @ sK3 @ cHH_1)) = $true)),
% 2.65/0.79 introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
% 2.65/0.79 thf(f51,plain,(
% 2.65/0.79 (((el1 @ sK3 @ cHH_1)) = $true) | ~spl5_2),
% 2.65/0.79 inference(avatar_component_clause,[],[f49])).
% 2.65/0.79 thf(f52,plain,(
% 2.65/0.79 spl5_2 | spl5_1),
% 2.65/0.79 inference(avatar_split_clause,[],[f24,f44,f49])).
% 2.65/0.79 thf(f54,definition,(
% 2.65/0.79 spl5_3 <=> (((cHOM_FROM_SS_PRIME @ cPHI_2)) = $true)),
% 2.65/0.79 introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition])).
% 2.65/0.79 thf(f56,plain,(
% 2.65/0.79 (((cHOM_FROM_SS_PRIME @ cPHI_2)) = $true) | ~spl5_3),
% 2.65/0.79 inference(avatar_component_clause,[],[f54])).
% 2.65/0.79 thf(f57,plain,(
% 2.65/0.79 spl5_3),
% 2.65/0.79 inference(avatar_split_clause,[],[f27,f54])).
% 2.65/0.79 thf(f59,definition,(
% 2.65/0.79 spl5_4 <=> (((cHOM_FROM_SS_PRIME @ cPHI_1)) = $true)),
% 2.65/0.79 introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition])).
% 2.65/0.79 thf(f61,plain,(
% 2.65/0.79 (((cHOM_FROM_SS_PRIME @ cPHI_1)) = $true) | ~spl5_4),
% 2.65/0.79 inference(avatar_component_clause,[],[f59])).
% 2.65/0.79 thf(f62,plain,(
% 2.65/0.79 spl5_4),
% 2.65/0.79 inference(avatar_split_clause,[],[f14,f59])).
% 2.65/0.79 thf(f64,definition,(
% 2.65/0.79 spl5_5 <=> (((cTIMES @ (cBIGPHI @ sK3) @ (cBIGPHI @ sK2))) = ((cBIGPHI @ (cTIMES @ sK3 @ sK2))))),
% 2.65/0.79 introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition])).
% 2.65/0.79 thf(f66,plain,(
% 2.65/0.79 (((cTIMES @ (cBIGPHI @ sK3) @ (cBIGPHI @ sK2))) != ((cBIGPHI @ (cTIMES @ sK3 @ sK2)))) | spl5_5),
% 2.65/0.79 inference(avatar_component_clause,[],[f64])).
% 2.65/0.79 thf(f67,plain,(
% 2.65/0.79 spl5_1 | ~spl5_5),
% 2.65/0.79 inference(avatar_split_clause,[],[f25,f64,f44])).
% 2.65/0.79 thf(f69,definition,(
% 2.65/0.79 spl5_6 <=> ($true = ((el1 @ sK2 @ cHH_1)))),
% 2.65/0.79 introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition])).
% 2.65/0.79 thf(f71,plain,(
% 2.65/0.79 ($true = ((el1 @ sK2 @ cHH_1))) | ~spl5_6),
% 2.65/0.79 inference(avatar_component_clause,[],[f69])).
% 2.65/0.79 thf(f72,plain,(
% 2.65/0.79 spl5_6 | spl5_1),
% 2.65/0.79 inference(avatar_split_clause,[],[f23,f44,f69])).
% 2.65/0.79 thf(f77,plain,(
% 2.65/0.79 (((cPHI_1 @ (sK4 @ sK2))) = sK2) | ~spl5_6),
% 2.65/0.79 inference(unit_resulting_resolution,[],[f17,f71])).
% 2.65/0.79 thf(f79,plain,(
% 2.65/0.79 (((cPHI_1 @ (sK4 @ sK3))) = sK3) | ($true != $true) | ~spl5_2),
% 2.65/0.79 inference(superposition,[],[f17,f51])).
% 2.65/0.79 thf(f81,plain,(
% 2.65/0.79 (((cPHI_1 @ (sK4 @ sK3))) = sK3) | ~spl5_2),
% 2.65/0.79 inference(trivial_inequality_removal,[],[f79])).
% 2.65/0.79 thf(f84,definition,(
% 2.65/0.79 spl5_8 <=> (((cPHI_1 @ (sK4 @ sK2))) = sK2)),
% 2.65/0.79 introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition])).
% 2.65/0.79 thf(f86,plain,(
% 2.65/0.79 (((cPHI_1 @ (sK4 @ sK2))) = sK2) | ~spl5_8),
% 2.65/0.79 inference(avatar_component_clause,[],[f84])).
% 2.65/0.79 thf(f87,plain,(
% 2.65/0.79 spl5_8 | ~spl5_6),
% 2.65/0.79 inference(avatar_split_clause,[],[f77,f69,f84])).
% 2.65/0.79 thf(f89,definition,(
% 2.65/0.79 spl5_9 <=> (((cPHI_1 @ (sK4 @ sK3))) = sK3)),
% 2.65/0.79 introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition])).
% 2.65/0.79 thf(f91,plain,(
% 2.65/0.79 (((cPHI_1 @ (sK4 @ sK3))) = sK3) | ~spl5_9),
% 2.65/0.79 inference(avatar_component_clause,[],[f89])).
% 2.65/0.79 thf(f92,plain,(
% 2.65/0.79 spl5_9 | ~spl5_2),
% 2.65/0.79 inference(avatar_split_clause,[],[f81,f49,f89])).
% 2.65/0.79 thf(f93,plain,(
% 2.65/0.79 (((cBIGHI @ sK2)) = ((cBIGPHI @ sK2))) | ~spl5_6),
% 2.65/0.79 inference(unit_resulting_resolution,[],[f40,f71])).
% 2.65/0.79 thf(f95,plain,(
% 2.65/0.79 ($true != $true) | (((cBIGHI @ sK3)) = ((cBIGPHI @ sK3))) | ~spl5_2),
% 2.65/0.79 inference(superposition,[],[f40,f51])).
% 2.65/0.79 thf(f97,plain,(
% 2.65/0.79 (((cBIGHI @ sK3)) = ((cBIGPHI @ sK3))) | ~spl5_2),
% 2.65/0.79 inference(trivial_inequality_removal,[],[f95])).
% 2.65/0.79 thf(f100,definition,(
% 2.65/0.79 spl5_10 <=> (((cBIGHI @ sK2)) = ((cBIGPHI @ sK2)))),
% 2.65/0.79 introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition])).
% 2.65/0.79 thf(f102,plain,(
% 2.65/0.79 (((cBIGHI @ sK2)) = ((cBIGPHI @ sK2))) | ~spl5_10),
% 2.65/0.79 inference(avatar_component_clause,[],[f100])).
% 2.65/0.79 thf(f103,plain,(
% 2.65/0.79 spl5_10 | ~spl5_6),
% 2.65/0.79 inference(avatar_split_clause,[],[f93,f69,f100])).
% 2.65/0.79 thf(f105,definition,(
% 2.65/0.79 spl5_11 <=> (((cBIGHI @ sK3)) = ((cBIGPHI @ sK3)))),
% 2.65/0.79 introduced(definition,[new_symbols(definition,[spl5_11])],[avatar_definition])).
% 2.65/0.79 thf(f107,plain,(
% 2.65/0.79 (((cBIGHI @ sK3)) = ((cBIGPHI @ sK3))) | ~spl5_11),
% 2.65/0.79 inference(avatar_component_clause,[],[f105])).
% 2.65/0.79 thf(f108,plain,(
% 2.65/0.79 spl5_11 | ~spl5_2),
% 2.65/0.79 inference(avatar_split_clause,[],[f97,f49,f105])).
% 2.65/0.79 thf(f121,plain,(
% 2.65/0.79 ($true = ((el1 @ (sK4 @ sK2) @ cSS_PRIME))) | ~spl5_6),
% 2.65/0.79 inference(unit_resulting_resolution,[],[f16,f71])).
% 2.65/0.79 thf(f122,plain,(
% 2.65/0.79 ($true = ((el1 @ (sK4 @ sK3) @ cSS_PRIME))) | ~spl5_2),
% 2.65/0.79 inference(unit_resulting_resolution,[],[f16,f51])).
% 2.65/0.79 thf(f128,definition,(
% 2.65/0.79 spl5_12 <=> ($true = ((el1 @ (sK4 @ sK3) @ cSS_PRIME)))),
% 2.65/0.79 introduced(definition,[new_symbols(definition,[spl5_12])],[avatar_definition])).
% 2.65/0.79 thf(f130,plain,(
% 2.65/0.79 ($true = ((el1 @ (sK4 @ sK3) @ cSS_PRIME))) | ~spl5_12),
% 2.65/0.79 inference(avatar_component_clause,[],[f128])).
% 2.65/0.79 thf(f131,plain,(
% 2.65/0.79 spl5_12 | ~spl5_2),
% 2.65/0.79 inference(avatar_split_clause,[],[f122,f49,f128])).
% 2.65/0.79 thf(f133,definition,(
% 2.65/0.79 spl5_13 <=> ($true = ((el1 @ (sK4 @ sK2) @ cSS_PRIME)))),
% 2.65/0.79 introduced(definition,[new_symbols(definition,[spl5_13])],[avatar_definition])).
% 2.65/0.79 thf(f135,plain,(
% 2.65/0.79 ($true = ((el1 @ (sK4 @ sK2) @ cSS_PRIME))) | ~spl5_13),
% 2.65/0.79 inference(avatar_component_clause,[],[f133])).
% 2.65/0.79 thf(f136,plain,(
% 2.65/0.79 spl5_13 | ~spl5_6),
% 2.65/0.79 inference(avatar_split_clause,[],[f121,f69,f133])).
% 2.65/0.79 thf(f153,plain,(
% 2.65/0.79 ($true = ((el1 @ (cTIMES @ sK3 @ sK2) @ cHH_1))) | (~spl5_2 | ~spl5_6)),
% 2.65/0.79 inference(unit_resulting_resolution,[],[f15,f51,f71])).
% 2.65/0.79 thf(f177,definition,(
% 2.65/0.79 spl5_19 <=> ($true = ((el1 @ (cTIMES @ sK3 @ sK2) @ cHH_1)))),
% 2.65/0.79 introduced(definition,[new_symbols(definition,[spl5_19])],[avatar_definition])).
% 2.65/0.79 thf(f179,plain,(
% 2.65/0.79 ($true = ((el1 @ (cTIMES @ sK3 @ sK2) @ cHH_1))) | ~spl5_19),
% 2.65/0.79 inference(avatar_component_clause,[],[f177])).
% 2.65/0.79 thf(f180,plain,(
% 2.65/0.79 spl5_19 | ~spl5_2 | ~spl5_6),
% 2.65/0.79 inference(avatar_split_clause,[],[f153,f69,f49,f177])).
% 2.65/0.79 thf(f185,plain,(
% 2.65/0.79 (((cTIMES @ (cBIGPHI @ sK3) @ (cBIGHI @ sK2))) != ((cBIGPHI @ (cTIMES @ sK3 @ sK2)))) | (spl5_5 | ~spl5_10)),
% 2.65/0.79 inference(backward_demodulation,[],[f66,f102])).
% 2.65/0.79 thf(f187,definition,(
% 2.65/0.79 spl5_20 <=> (((cTIMES @ (cBIGPHI @ sK3) @ (cBIGHI @ sK2))) = ((cBIGPHI @ (cTIMES @ sK3 @ sK2))))),
% 2.65/0.79 introduced(definition,[new_symbols(definition,[spl5_20])],[avatar_definition])).
% 2.65/0.79 thf(f189,plain,(
% 2.65/0.79 (((cTIMES @ (cBIGPHI @ sK3) @ (cBIGHI @ sK2))) != ((cBIGPHI @ (cTIMES @ sK3 @ sK2)))) | spl5_20),
% 2.65/0.79 inference(avatar_component_clause,[],[f187])).
% 2.65/0.79 thf(f190,plain,(
% 2.65/0.79 ~spl5_20 | spl5_5 | ~spl5_10),
% 2.65/0.79 inference(avatar_split_clause,[],[f185,f100,f64,f187])).
% 2.65/0.79 thf(f191,plain,(
% 2.65/0.79 (((cTIMES @ (cBIGHI @ sK3) @ (cBIGHI @ sK2))) != ((cBIGPHI @ (cTIMES @ sK3 @ sK2)))) | (~spl5_11 | spl5_20)),
% 2.65/0.79 inference(backward_demodulation,[],[f189,f107])).
% 2.65/0.79 thf(f193,definition,(
% 2.65/0.79 spl5_21 <=> (((cTIMES @ (cBIGHI @ sK3) @ (cBIGHI @ sK2))) = ((cBIGPHI @ (cTIMES @ sK3 @ sK2))))),
% 2.65/0.79 introduced(definition,[new_symbols(definition,[spl5_21])],[avatar_definition])).
% 2.65/0.79 thf(f196,plain,(
% 2.65/0.79 ~spl5_21 | ~spl5_11 | spl5_20),
% 2.65/0.79 inference(avatar_split_clause,[],[f191,f187,f105,f193])).
% 2.65/0.79 thf(f205,plain,(
% 2.65/0.79 (((cPHI_2 @ (sK4 @ sK3))) = ((cBIGPHI @ (cPHI_1 @ (sK4 @ sK3))))) | ($true != $true) | ~spl5_12),
% 2.65/0.79 inference(superposition,[],[f19,f130])).
% 2.65/0.79 thf(f206,plain,(
% 2.65/0.79 (((cPHI_2 @ (sK4 @ sK3))) = ((cBIGPHI @ (cPHI_1 @ (sK4 @ sK3))))) | ~spl5_12),
% 2.65/0.79 inference(trivial_inequality_removal,[],[f205])).
% 2.65/0.79 thf(f210,plain,(
% 2.65/0.79 (((cPHI_2 @ (sK4 @ sK3))) = ((cBIGPHI @ sK3))) | (~spl5_9 | ~spl5_12)),
% 2.65/0.79 inference(forward_demodulation,[],[f206,f91])).
% 2.65/0.79 thf(f224,plain,(
% 2.65/0.79 (((cBIGHI @ sK3)) = ((cPHI_2 @ (sK4 @ sK3)))) | (~spl5_9 | ~spl5_11 | ~spl5_12)),
% 2.65/0.79 inference(forward_demodulation,[],[f210,f107])).
% 2.65/0.79 thf(f227,definition,(
% 2.65/0.79 spl5_24 <=> (((cBIGHI @ sK3)) = ((cPHI_2 @ (sK4 @ sK3))))),
% 2.65/0.79 introduced(definition,[new_symbols(definition,[spl5_24])],[avatar_definition])).
% 2.65/0.79 thf(f229,plain,(
% 2.65/0.79 (((cBIGHI @ sK3)) = ((cPHI_2 @ (sK4 @ sK3)))) | ~spl5_24),
% 2.65/0.79 inference(avatar_component_clause,[],[f227])).
% 2.65/0.79 thf(f230,plain,(
% 2.65/0.79 spl5_24 | ~spl5_9 | ~spl5_11 | ~spl5_12),
% 2.65/0.79 inference(avatar_split_clause,[],[f224,f128,f105,f89,f227])).
% 2.65/0.79 thf(f233,plain,(
% 2.65/0.79 ($true = ((el1 @ (cTIMES @ (sK4 @ sK3) @ (sK4 @ sK2)) @ cSS_PRIME))) | (~spl5_12 | ~spl5_13)),
% 2.65/0.79 inference(unit_resulting_resolution,[],[f21,f130,f135])).
% 2.65/0.79 thf(f241,plain,(
% 2.65/0.79 (((cPHI_2 @ (sK4 @ sK2))) = ((cBIGPHI @ (cPHI_1 @ (sK4 @ sK2))))) | ($true != $true) | ~spl5_13),
% 2.65/0.79 inference(superposition,[],[f19,f135])).
% 2.65/0.79 thf(f243,plain,(
% 2.65/0.79 (((cPHI_2 @ (sK4 @ sK2))) = ((cBIGPHI @ (cPHI_1 @ (sK4 @ sK2))))) | ~spl5_13),
% 2.65/0.79 inference(trivial_inequality_removal,[],[f241])).
% 2.65/0.79 thf(f247,definition,(
% 2.65/0.79 spl5_25 <=> ($true = ((el1 @ (cTIMES @ (sK4 @ sK3) @ (sK4 @ sK2)) @ cSS_PRIME)))),
% 2.65/0.79 introduced(definition,[new_symbols(definition,[spl5_25])],[avatar_definition])).
% 2.65/0.79 thf(f249,plain,(
% 2.65/0.79 ($true = ((el1 @ (cTIMES @ (sK4 @ sK3) @ (sK4 @ sK2)) @ cSS_PRIME))) | ~spl5_25),
% 2.65/0.79 inference(avatar_component_clause,[],[f247])).
% 2.65/0.79 thf(f250,plain,(
% 2.65/0.79 spl5_25 | ~spl5_12 | ~spl5_13),
% 2.65/0.79 inference(avatar_split_clause,[],[f233,f133,f128,f247])).
% 2.65/0.79 thf(f257,plain,(
% 2.65/0.79 (((cPHI_2 @ (sK4 @ sK2))) = ((cBIGPHI @ sK2))) | (~spl5_8 | ~spl5_13)),
% 2.65/0.79 inference(forward_demodulation,[],[f243,f86])).
% 2.65/0.79 thf(f270,plain,(
% 2.65/0.79 (((cBIGHI @ sK2)) = ((cPHI_2 @ (sK4 @ sK2)))) | (~spl5_8 | ~spl5_10 | ~spl5_13)),
% 2.65/0.79 inference(forward_demodulation,[],[f257,f102])).
% 2.65/0.79 thf(f273,definition,(
% 2.65/0.79 spl5_29 <=> (((cBIGHI @ sK2)) = ((cPHI_2 @ (sK4 @ sK2))))),
% 2.65/0.79 introduced(definition,[new_symbols(definition,[spl5_29])],[avatar_definition])).
% 2.65/0.79 thf(f275,plain,(
% 2.65/0.79 (((cBIGHI @ sK2)) = ((cPHI_2 @ (sK4 @ sK2)))) | ~spl5_29),
% 2.65/0.79 inference(avatar_component_clause,[],[f273])).
% 2.65/0.79 thf(f276,plain,(
% 2.65/0.79 spl5_29 | ~spl5_8 | ~spl5_10 | ~spl5_13),
% 2.65/0.79 inference(avatar_split_clause,[],[f270,f133,f100,f84,f273])).
% 2.65/0.79 thf(f536,plain,(
% 2.65/0.79 (((cTIMES @ sK3 @ sK2)) = ((cPHI_1 @ (sK4 @ (cTIMES @ sK3 @ sK2))))) | ~spl5_19),
% 2.65/0.79 inference(unit_resulting_resolution,[],[f17,f179])).
% 2.65/0.79 thf(f573,definition,(
% 2.65/0.79 spl5_70 <=> (((cTIMES @ sK3 @ sK2)) = ((cPHI_1 @ (sK4 @ (cTIMES @ sK3 @ sK2)))))),
% 2.65/0.79 introduced(definition,[new_symbols(definition,[spl5_70])],[avatar_definition])).
% 2.65/0.79 thf(f576,plain,(
% 2.65/0.79 spl5_70 | ~spl5_19),
% 2.65/0.79 inference(avatar_split_clause,[],[f536,f177,f573])).
% 2.65/0.79 thf(f1171,plain,(
% 2.65/0.79 (((cBIGPHI @ (cPHI_1 @ (cTIMES @ (sK4 @ sK3) @ (sK4 @ sK2))))) = ((cPHI_2 @ (cTIMES @ (sK4 @ sK3) @ (sK4 @ sK2))))) | ~spl5_25),
% 2.65/0.79 inference(unit_resulting_resolution,[],[f19,f249])).
% 2.65/0.79 thf(f1216,definition,(
% 2.65/0.79 spl5_148 <=> (((cBIGPHI @ (cPHI_1 @ (cTIMES @ (sK4 @ sK3) @ (sK4 @ sK2))))) = ((cPHI_2 @ (cTIMES @ (sK4 @ sK3) @ (sK4 @ sK2)))))),
% 2.65/0.79 introduced(definition,[new_symbols(definition,[spl5_148])],[avatar_definition])).
% 2.65/0.79 thf(f1219,plain,(
% 2.65/0.79 spl5_148 | ~spl5_25),
% 2.65/0.79 inference(avatar_split_clause,[],[f1171,f247,f1216])).
% 2.65/0.79 thf(f2893,plain,(
% 2.65/0.79 (((cTIMES @ (cPHI_2 @ (sK4 @ sK3)) @ (cPHI_2 @ (sK4 @ sK2)))) = ((cPHI_2 @ (cTIMES @ (sK4 @ sK3) @ (sK4 @ sK2))))) | (~spl5_3 | ~spl5_12 | ~spl5_13)),
% 2.65/0.79 inference(unit_resulting_resolution,[],[f28,f56,f135,f130])).
% 2.65/0.79 thf(f2894,plain,(
% 2.65/0.79 (((cTIMES @ (cPHI_1 @ (sK4 @ sK3)) @ (cPHI_1 @ (sK4 @ sK2)))) = ((cPHI_1 @ (cTIMES @ (sK4 @ sK3) @ (sK4 @ sK2))))) | (~spl5_4 | ~spl5_12 | ~spl5_13)),
% 2.65/0.79 inference(unit_resulting_resolution,[],[f28,f61,f135,f130])).
% 2.65/0.79 thf(f3625,plain,(
% 2.65/0.79 (((cTIMES @ sK3 @ (cPHI_1 @ (sK4 @ sK2)))) = ((cPHI_1 @ (cTIMES @ (sK4 @ sK3) @ (sK4 @ sK2))))) | (~spl5_4 | ~spl5_9 | ~spl5_12 | ~spl5_13)),
% 2.65/0.79 inference(forward_demodulation,[],[f2894,f91])).
% 2.65/0.79 thf(f3670,plain,(
% 2.65/0.79 (((cTIMES @ (cBIGHI @ sK3) @ (cPHI_2 @ (sK4 @ sK2)))) = ((cPHI_2 @ (cTIMES @ (sK4 @ sK3) @ (sK4 @ sK2))))) | (~spl5_3 | ~spl5_12 | ~spl5_13 | ~spl5_24)),
% 2.65/0.79 inference(forward_demodulation,[],[f2893,f229])).
% 2.65/0.79 thf(f4112,plain,(
% 2.65/0.79 (((cPHI_1 @ (cTIMES @ (sK4 @ sK3) @ (sK4 @ sK2)))) = ((cTIMES @ sK3 @ sK2))) | (~spl5_4 | ~spl5_8 | ~spl5_9 | ~spl5_12 | ~spl5_13)),
% 2.65/0.79 inference(forward_demodulation,[],[f3625,f86])).
% 2.65/0.79 thf(f4133,plain,(
% 2.65/0.79 (((cTIMES @ (cBIGHI @ sK3) @ (cBIGHI @ sK2))) = ((cPHI_2 @ (cTIMES @ (sK4 @ sK3) @ (sK4 @ sK2))))) | (~spl5_3 | ~spl5_12 | ~spl5_13 | ~spl5_24 | ~spl5_29)),
% 2.65/0.79 inference(forward_demodulation,[],[f3670,f275])).
% 2.65/0.79 thf(f4379,definition,(
% 2.65/0.79 spl5_586 <=> (((cPHI_1 @ (cTIMES @ (sK4 @ sK3) @ (sK4 @ sK2)))) = ((cTIMES @ sK3 @ sK2)))),
% 2.65/0.79 introduced(definition,[new_symbols(definition,[spl5_586])],[avatar_definition])).
% 2.65/0.79 thf(f4382,plain,(
% 2.65/0.79 spl5_586 | ~spl5_4 | ~spl5_8 | ~spl5_9 | ~spl5_12 | ~spl5_13),
% 2.65/0.79 inference(avatar_split_clause,[],[f4112,f133,f128,f89,f84,f59,f4379])).
% 2.65/0.79 thf(f4384,definition,(
% 2.65/0.79 spl5_587 <=> (((cTIMES @ (cBIGHI @ sK3) @ (cBIGHI @ sK2))) = ((cPHI_2 @ (cTIMES @ (sK4 @ sK3) @ (sK4 @ sK2)))))),
% 2.65/0.79 introduced(definition,[new_symbols(definition,[spl5_587])],[avatar_definition])).
% 2.65/0.79 thf(f4387,plain,(
% 2.65/0.79 spl5_587 | ~spl5_3 | ~spl5_12 | ~spl5_13 | ~spl5_24 | ~spl5_29),
% 2.65/0.79 inference(avatar_split_clause,[],[f4133,f273,f227,f133,f128,f54,f4384])).
% 2.65/0.79 thf(f4435,definition,(
% 2.65/0.79 (((cPHI_1 @ (cTIMES @ (sK4 @ sK3) @ (sK4 @ sK2)))) != ((cTIMES @ sK3 @ sK2))) | (((cTIMES @ sK3 @ sK2)) != ((cPHI_1 @ (sK4 @ (cTIMES @ sK3 @ sK2))))) | (((cTIMES @ (cBIGHI @ sK3) @ (cBIGHI @ sK2))) != ((cPHI_2 @ (cTIMES @ (sK4 @ sK3) @ (sK4 @ sK2))))) | (((cBIGPHI @ (cPHI_1 @ (cTIMES @ (sK4 @ sK3) @ (sK4 @ sK2))))) != ((cPHI_2 @ (cTIMES @ (sK4 @ sK3) @ (sK4 @ sK2))))) | (((cTIMES @ (cBIGHI @ sK3) @ (cBIGHI @ sK2))) = ((cBIGPHI @ (cTIMES @ sK3 @ sK2))))),
% 2.65/0.79 introduced(theory,[theory_tautology_sat_conflict])).
% 2.65/0.79 cnf(s1, plain, ~spl5_1, inference(sat_conversion,[],[f47])).
% 2.65/0.79 cnf(s2, plain, spl5_1 | spl5_2, inference(sat_conversion,[],[f52])).
% 2.65/0.79 cnf(s3, plain, spl5_3, inference(sat_conversion,[],[f57])).
% 2.65/0.79 cnf(s4, plain, spl5_4, inference(sat_conversion,[],[f62])).
% 2.65/0.79 cnf(s5, plain, spl5_1 | ~spl5_5, inference(sat_conversion,[],[f67])).
% 2.65/0.79 cnf(s6, plain, spl5_1 | spl5_6, inference(sat_conversion,[],[f72])).
% 2.65/0.79 cnf(s8, plain, ~spl5_6 | spl5_8, inference(sat_conversion,[],[f87])).
% 2.65/0.79 cnf(s9, plain, ~spl5_2 | spl5_9, inference(sat_conversion,[],[f92])).
% 2.65/0.79 cnf(s12, plain, ~spl5_6 | spl5_10, inference(sat_conversion,[],[f103])).
% 2.65/0.79 cnf(s13, plain, ~spl5_2 | spl5_11, inference(sat_conversion,[],[f108])).
% 2.65/0.79 cnf(s16, plain, ~spl5_2 | spl5_12, inference(sat_conversion,[],[f131])).
% 2.65/0.79 cnf(s17, plain, ~spl5_6 | spl5_13, inference(sat_conversion,[],[f136])).
% 2.65/0.79 cnf(s27, plain, ~spl5_2 | ~spl5_6 | spl5_19, inference(sat_conversion,[],[f180])).
% 2.65/0.79 cnf(s28, plain, spl5_5 | ~spl5_10 | ~spl5_20, inference(sat_conversion,[],[f190])).
% 2.65/0.79 cnf(s29, plain, ~spl5_11 | spl5_20 | ~spl5_21, inference(sat_conversion,[],[f196])).
% 2.65/0.79 cnf(s34, plain, ~spl5_9 | ~spl5_11 | ~spl5_12 | spl5_24, inference(sat_conversion,[],[f230])).
% 2.65/0.79 cnf(s36, plain, ~spl5_12 | ~spl5_13 | spl5_25, inference(sat_conversion,[],[f250])).
% 2.65/0.79 cnf(s42, plain, ~spl5_8 | ~spl5_10 | ~spl5_13 | spl5_29, inference(sat_conversion,[],[f276])).
% 2.65/0.79 cnf(s99, plain, ~spl5_19 | spl5_70, inference(sat_conversion,[],[f576])).
% 2.65/0.79 cnf(s217, plain, ~spl5_25 | spl5_148, inference(sat_conversion,[],[f1219])).
% 2.65/0.79 cnf(s739, plain, ~spl5_4 | ~spl5_8 | ~spl5_9 | ~spl5_12 | ~spl5_13 | spl5_586, inference(sat_conversion,[],[f4382])).
% 2.65/0.79 cnf(s740, plain, ~spl5_3 | ~spl5_12 | ~spl5_13 | ~spl5_24 | ~spl5_29 | spl5_587, inference(sat_conversion,[],[f4387])).
% 2.65/0.79 cnf(s752, plain, spl5_21 | ~spl5_70 | ~spl5_148 | ~spl5_586 | ~spl5_587, inference(sat_conversion,[],[f4435])).
% 2.65/0.79 cnf(s754, plain, spl5_6, inference(rat,[],[s6,s1])).
% 2.65/0.79 cnf(s755, plain, ~spl5_5, inference(rat,[],[s5,s1])).
% 2.65/0.79 cnf(s756, plain, spl5_2, inference(rat,[],[s2,s1])).
% 2.65/0.79 cnf(s759, plain, spl5_13, inference(rat,[],[s17,s754])).
% 2.65/0.79 cnf(s760, plain, spl5_10, inference(rat,[],[s12,s754])).
% 2.65/0.79 cnf(s761, plain, spl5_8, inference(rat,[],[s8,s754])).
% 2.65/0.79 cnf(s762, plain, spl5_19, inference(rat,[],[s27,s754,s756])).
% 2.65/0.79 cnf(s766, plain, spl5_12, inference(rat,[],[s16,s756])).
% 2.65/0.79 cnf(s767, plain, spl5_11, inference(rat,[],[s13,s756])).
% 2.65/0.79 cnf(s768, plain, spl5_9, inference(rat,[],[s9,s756])).
% 2.65/0.79 cnf(s781, plain, ~spl5_20, inference(rat,[],[s28,s755,s760])).
% 2.65/0.79 cnf(s787, plain, spl5_29, inference(rat,[],[s42,s760,s759,s761])).
% 2.65/0.79 cnf(s794, plain, spl5_70, inference(rat,[],[s99,s762])).
% 2.65/0.79 cnf(s828, plain, spl5_25, inference(rat,[],[s36,s759,s766])).
% 2.65/0.79 cnf(s849, plain, spl5_24, inference(rat,[],[s34,s767,s766,s768])).
% 2.65/0.79 cnf(s850, plain, spl5_586, inference(rat,[],[s739,s761,s759,s766,s4,s768])).
% 2.65/0.79 cnf(s880, plain, ~spl5_21, inference(rat,[],[s29,s767,s781])).
% 2.65/0.79 cnf(s1261, plain, spl5_148, inference(rat,[],[s217,s828])).
% 2.65/0.79 cnf(s1340, plain, spl5_587, inference(rat,[],[s740,s766,s787,s759,s3,s849])).
% 2.65/0.79 cnf(s1344, plain, $false, inference(rat,[],[s752,s1340,s850,s794,s1261,s880])).
% 2.65/0.79 thf(f4437,plain,(
% 2.65/0.79 $false),
% 2.65/0.79 inference(avatar_sat_refutation,[],[s1344])).
% 2.65/0.79 % SZS output end Proof for theBenchmark
% 2.65/0.79 % (320936)------------------------------
% 2.65/0.79 % (320936)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.65/0.79 % (320936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.65/0.79 % (320936)CaDiCaL version: 2.1.3
% 2.65/0.79 % (320936)Termination reason: Refutation
% 2.65/0.79 % (320936)Time elapsed: 0.165 s
% 2.65/0.79 % (320936)Peak memory usage: 16 MB
% 2.65/0.79 % (320936)Instructions burned: 199 (million)
% 2.65/0.79 % (320849)Success in time 0.57 s
% 2.65/0.79 % Vampire exiting
%------------------------------------------------------------------------------