%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP108^2 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:08:22 AM UTC 2026
% Result : Theorem 0.90s 0.49s
% Output : Refutation 0.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP108^2 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n011.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 19:54:47 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.21/0.30 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
% 0.90/0.46 % (562280)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.90/0.46 % (562286)lrs+10_16_si=on:nwc=1.5:random_seed=1973586700:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.90/0.46 % (562291)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.90/0.46 % (562291)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
% 0.90/0.46 % (562286)Instruction limit reached!
% 0.90/0.46 % (562286)------------------------------
% 0.90/0.46 % (562286)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.46 % (562286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.46 % (562286)CaDiCaL version: 2.1.3
% 0.90/0.46 % (562286)Termination reason: Instruction limit
% 0.90/0.46 % (562286)Termination phase: shuffling
% 0.90/0.46 % (562286)Time elapsed: 0.005 s
% 0.90/0.46 % (562286)Peak memory usage: 10 MB
% 0.90/0.46 % (562286)Instructions burned: 23 (million)
% 0.90/0.46 % (562285)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1582370299:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.90/0.46 % (562287)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2226699780:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.90/0.46 % (562289)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2669174772:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.90/0.46 % (562288)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=1244106575: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)
% 0.90/0.46 % (562290)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3816640188:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.90/0.46 % (562291)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=4051117746:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.90/0.46 % (562287)Instruction limit reached!
% 0.90/0.46 % (562287)------------------------------
% 0.90/0.46 % (562287)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.46 % (562287)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.46 % (562287)CaDiCaL version: 2.1.3
% 0.90/0.46 % (562287)Termination reason: Instruction limit
% 0.90/0.46 % (562287)Termination phase: shuffling
% 0.90/0.46 % (562287)Time elapsed: 0.002 s
% 0.90/0.46 % (562287)Peak memory usage: 10 MB
% 0.90/0.46 % (562287)Instructions burned: 4 (million)
% 0.90/0.46 % (562293)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1111701564:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.90/0.46 % (562293)Instruction limit reached!
% 0.90/0.46 % (562293)------------------------------
% 0.90/0.46 % (562293)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.46 % (562293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.46 % (562293)CaDiCaL version: 2.1.3
% 0.90/0.46 % (562293)Termination reason: Instruction limit
% 0.90/0.46 % (562293)Termination phase: shuffling
% 0.90/0.46 % (562293)Time elapsed: 0.001 s
% 0.90/0.46 % (562293)Peak memory usage: 10 MB
% 0.90/0.46 % (562293)Instructions burned: 4 (million)
% 0.90/0.46 % (562289)Instruction limit reached!
% 0.90/0.46 % (562289)------------------------------
% 0.90/0.46 % (562289)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.46 % (562289)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.46 % (562289)CaDiCaL version: 2.1.3
% 0.90/0.46 % (562289)Termination reason: Instruction limit
% 0.90/0.46 % (562289)Termination phase: shuffling
% 0.90/0.46 % (562289)Time elapsed: 0.011 s
% 0.90/0.46 % (562289)Peak memory usage: 10 MB
% 0.90/0.46 % (562289)Instructions burned: 26 (million)
% 0.90/0.46 % (562302)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.90/0.46 % (562302)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2492808196:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.90/0.48 % (562300)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=528571532:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.90/0.48 % (562302)Instruction limit reached!
% 0.90/0.48 % (562302)------------------------------
% 0.90/0.48 % (562302)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.48 % (562302)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.48 % (562302)CaDiCaL version: 2.1.3
% 0.90/0.48 % (562302)Termination reason: Instruction limit
% 0.90/0.48 % (562302)Termination phase: shuffling
% 0.90/0.48 % (562302)Time elapsed: 0.002 s
% 0.90/0.48 % (562302)Peak memory usage: 10 MB
% 0.90/0.48 % (562302)Instructions burned: 9 (million)
% 0.90/0.48 % (562300)Instruction limit reached!
% 0.90/0.48 % (562300)------------------------------
% 0.90/0.48 % (562300)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.48 % (562300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.48 % (562300)CaDiCaL version: 2.1.3
% 0.90/0.48 % (562300)Termination reason: Instruction limit
% 0.90/0.48 % (562300)Termination phase: shuffling
% 0.90/0.48 % (562300)Time elapsed: 0.003 s
% 0.90/0.48 % (562300)Peak memory usage: 10 MB
% 0.90/0.48 % (562300)Instructions burned: 6 (million)
% 0.90/0.48 % (562303)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2134654457:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.90/0.48 % (562306)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
% 0.90/0.48 % (562306)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.90/0.48 % (562290)Instruction limit reached!
% 0.90/0.48 % (562290)------------------------------
% 0.90/0.48 % (562290)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.48 % (562290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.48 % (562290)CaDiCaL version: 2.1.3
% 0.90/0.48 % (562290)Termination reason: Instruction limit
% 0.90/0.48 % (562290)Termination phase: Preprocessing 2
% 0.90/0.48 % (562290)Time elapsed: 0.032 s
% 0.90/0.48 % (562290)Peak memory usage: 11 MB
% 0.90/0.48 % (562290)Instructions burned: 76 (million)
% 0.90/0.48 % (562306)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=752531853:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.90/0.48 % (562285)Instruction limit reached!
% 0.90/0.48 % (562285)------------------------------
% 0.90/0.48 % (562285)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.48 % (562285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.48 % (562285)CaDiCaL version: 2.1.3
% 0.90/0.48 % (562285)Termination reason: Instruction limit
% 0.90/0.48 % (562285)Termination phase: Property scanning
% 0.90/0.48 % (562285)Time elapsed: 0.037 s
% 0.90/0.48 % (562285)Peak memory usage: 11 MB
% 0.90/0.48 % (562285)Instructions burned: 87 (million)
% 0.90/0.48 % (562303)Instruction limit reached!
% 0.90/0.48 % (562303)------------------------------
% 0.90/0.48 % (562303)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.48 % (562303)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.48 % (562303)CaDiCaL version: 2.1.3
% 0.90/0.48 % (562303)Termination reason: Instruction limit
% 0.90/0.48 % (562303)Termination phase: shuffling
% 0.90/0.48 % (562303)Time elapsed: 0.006 s
% 0.90/0.48 % (562303)Peak memory usage: 10 MB
% 0.90/0.48 % (562303)Instructions burned: 15 (million)
% 0.90/0.48 % (562306)Instruction limit reached!
% 0.90/0.48 % (562306)------------------------------
% 0.90/0.48 % (562306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.48 % (562306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.48 % (562306)CaDiCaL version: 2.1.3
% 0.90/0.48 % (562306)Termination reason: Instruction limit
% 0.90/0.48 % (562306)Termination phase: shuffling
% 0.90/0.48 % (562306)Time elapsed: 0.006 s
% 0.90/0.48 % (562306)Peak memory usage: 10 MB
% 0.90/0.48 % (562306)Instructions burned: 29 (million)
% 0.90/0.48 % (562307)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=367082231:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.90/0.48 % (562313)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3095684620:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.90/0.48 % (562310)lrs+10_1_si=on:cs=on:random_seed=87785214:i=8:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.90/0.48 % (562311)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.90/0.48 % (562311)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=4031191144:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.90/0.48 % (562312)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=4161125921:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.90/0.48 % (562310)Instruction limit reached!
% 0.90/0.48 % (562310)------------------------------
% 0.90/0.48 % (562310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.48 % (562310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.48 % (562310)CaDiCaL version: 2.1.3
% 0.90/0.48 % (562310)Termination reason: Instruction limit
% 0.90/0.48 % (562310)Termination phase: shuffling
% 0.90/0.48 % (562310)Time elapsed: 0.005 s
% 0.90/0.48 % (562310)Peak memory usage: 10 MB
% 0.90/0.48 % (562310)Instructions burned: 8 (million)
% 0.90/0.48 % (562311)Instruction limit reached!
% 0.90/0.48 % (562311)------------------------------
% 0.90/0.48 % (562311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.48 % (562311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.48 % (562311)CaDiCaL version: 2.1.3
% 0.90/0.48 % (562311)Termination reason: Instruction limit
% 0.90/0.48 % (562311)Termination phase: shuffling
% 0.90/0.48 % (562311)Time elapsed: 0.003 s
% 0.90/0.48 % (562311)Peak memory usage: 10 MB
% 0.90/0.48 % (562311)Instructions burned: 5 (million)
% 0.90/0.48 % (562291)Instruction limit reached!
% 0.90/0.48 % (562291)------------------------------
% 0.90/0.48 % (562291)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.48 % (562291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.48 % (562291)CaDiCaL version: 2.1.3
% 0.90/0.48 % (562291)Termination reason: Instruction limit
% 0.90/0.48 % (562291)Termination phase: Saturation
% 0.90/0.48 % (562291)Time elapsed: 0.067 s
% 0.90/0.48 % (562291)Peak memory usage: 13 MB
% 0.90/0.48 % (562291)Instructions burned: 157 (million)
% 0.90/0.48 % (562312)Instruction limit reached!
% 0.90/0.48 % (562312)------------------------------
% 0.90/0.48 % (562312)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.48 % (562312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.48 % (562312)CaDiCaL version: 2.1.3
% 0.90/0.48 % (562312)Termination reason: Instruction limit
% 0.90/0.48 % (562312)Termination phase: Property scanning
% 0.90/0.48 % (562312)Time elapsed: 0.017 s
% 0.90/0.48 % (562312)Peak memory usage: 10 MB
% 0.90/0.48 % (562312)Instructions burned: 40 (million)
% 0.90/0.48 % (562319)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1649989924:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.90/0.48 % (562320)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2028019952:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.90/0.48 % (562307)Instruction limit reached!
% 0.90/0.48 % (562307)------------------------------
% 0.90/0.48 % (562307)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.48 % (562307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.48 % (562307)CaDiCaL version: 2.1.3
% 0.90/0.48 % (562307)Termination reason: Instruction limit
% 0.90/0.48 % (562307)Termination phase: Property scanning
% 0.90/0.48 % (562307)Time elapsed: 0.036 s
% 0.90/0.48 % (562307)Peak memory usage: 11 MB
% 0.90/0.48 % (562307)Instructions burned: 88 (million)
% 0.90/0.48 % (562320)Instruction limit reached!
% 0.90/0.48 % (562320)------------------------------
% 0.90/0.48 % (562320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.48 % (562320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.48 % (562320)CaDiCaL version: 2.1.3
% 0.90/0.48 % (562320)Termination reason: Instruction limit
% 0.90/0.48 % (562320)Termination phase: shuffling
% 0.90/0.48 % (562320)Time elapsed: 0.007 s
% 0.90/0.48 % (562320)Peak memory usage: 10 MB
% 0.90/0.48 % (562320)Instructions burned: 16 (million)
% 0.90/0.48 % (562319)Instruction limit reached!
% 0.90/0.48 % (562319)------------------------------
% 0.90/0.48 % (562319)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.48 % (562319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.48 % (562319)CaDiCaL version: 2.1.3
% 0.90/0.48 % (562319)Termination reason: Instruction limit
% 0.90/0.48 % (562319)Termination phase: shuffling
% 0.90/0.48 % (562319)Time elapsed: 0.011 s
% 0.90/0.48 % (562319)Peak memory usage: 10 MB
% 0.90/0.48 % (562319)Instructions burned: 26 (million)
% 0.90/0.48 % (562321)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=665554646:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.90/0.48 % (562323)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2949708535:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.90/0.48 % (562325)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=543682413: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)
% 0.90/0.48 % (562288) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-562280-562288"...
% 0.90/0.48 % (562323)Instruction limit reached!
% 0.90/0.48 % (562323)------------------------------
% 0.90/0.48 % (562323)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.48 % (562323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.48 % (562323)CaDiCaL version: 2.1.3
% 0.90/0.48 % (562323)Termination reason: Instruction limit
% 0.90/0.48 % (562323)Termination phase: shuffling
% 0.90/0.48 % (562323)Time elapsed: 0.006 s
% 0.90/0.48 % (562323)Peak memory usage: 10 MB
% 0.90/0.48 % (562323)Instructions burned: 14 (million)
% 0.90/0.48 % (562325)Instruction limit reached!
% 0.90/0.48 % (562325)------------------------------
% 0.90/0.48 % (562325)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.48 % (562325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.48 % (562325)CaDiCaL version: 2.1.3
% 0.90/0.48 % (562325)Termination reason: Instruction limit
% 0.90/0.48 % (562325)Termination phase: shuffling
% 0.90/0.48 % (562325)Time elapsed: 0.002 s
% 0.90/0.48 % (562325)Peak memory usage: 10 MB
% 0.90/0.48 % (562325)Instructions burned: 4 (million)
% 0.90/0.48 % (562326)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3888782463:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.90/0.48 % (562327)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1403368893:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.90/0.48 % (562313)Instruction limit reached!
% 0.90/0.48 % (562313)------------------------------
% 0.90/0.48 % (562313)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.49 % (562313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.49 % (562313)CaDiCaL version: 2.1.3
% 0.90/0.49 % (562313)Termination reason: Instruction limit
% 0.90/0.49 % (562313)Termination phase: Saturation
% 0.90/0.49 % (562313)Time elapsed: 0.057 s
% 0.90/0.49 % (562313)Peak memory usage: 13 MB
% 0.90/0.49 % (562313)Instructions burned: 249 (million)
% 0.90/0.49 % (562288)...printing done.
% 0.90/0.49 % (562288)Refutation found. Thanks to Tanya!
% 0.90/0.49 % SZS status Theorem for theBenchmark
% 0.90/0.49 % SZS output start Proof for theBenchmark
% 0.90/0.49 thf(type_def_5, type, partia1265057091ct_ext: ($tType * $tType) > $tType).
% 0.90/0.49 thf(type_def_6, type, monoid_ext: ($tType * $tType) > $tType).
% 0.90/0.49 thf(type_def_7, type, ring_ext: ($tType * $tType) > $tType).
% 0.90/0.49 thf(type_def_8, type, product_prod: ($tType * $tType) > $tType).
% 0.90/0.49 thf(type_def_9, type, set: $tType > $tType).
% 0.90/0.49 thf(type_def_10, type, int: $tType).
% 0.90/0.49 thf(type_def_11, type, b: $tType).
% 0.90/0.49 thf(type_def_12, type, a: $tType).
% 0.90/0.49 thf(type_def_13, type, sTfun: ($tType * $tType) > $tType).
% 0.90/0.49 thf(func_def_0, type, group_add: !>[X0: $tType]:($o)).
% 0.90/0.49 thf(func_def_1, type, ab_group_add: !>[X0: $tType]:($o)).
% 0.90/0.49 thf(func_def_2, type, semigroup_add: !>[X0: $tType]:($o)).
% 0.90/0.49 thf(func_def_3, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 0.90/0.49 thf(func_def_4, type, ab_semigroup_add: !>[X0: $tType]:($o)).
% 0.90/0.49 thf(func_def_5, type, linordered_semidom: !>[X0: $tType]:($o)).
% 0.90/0.49 thf(func_def_6, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 0.90/0.49 thf(func_def_7, type, ordered_ab_group_add: !>[X0: $tType]:($o)).
% 0.90/0.49 thf(func_def_8, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 0.90/0.49 thf(func_def_9, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 0.90/0.49 thf(func_def_10, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 0.90/0.49 thf(func_def_11, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 0.90/0.49 thf(func_def_12, type, ordere236663937imp_le: !>[X0: $tType]:($o)).
% 0.90/0.49 thf(func_def_13, type, ordere623563068d_diff: !>[X0: $tType]:($o)).
% 0.90/0.49 thf(func_def_14, type, a_l_coset: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > X0 > set @ X0 > set @ X0))).
% 0.90/0.49 thf(func_def_15, type, additive_subgroup: !>[X0: $tType, X1: $tType]:((set @ X0 > partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > $o))).
% 0.90/0.49 thf(func_def_16, type, set_add: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > set @ X0 > set @ X0 > set @ X0))).
% 0.90/0.49 thf(func_def_17, type, partial_carrier: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ X1 > set @ X0))).
% 0.90/0.49 thf(func_def_18, type, mult: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ X1 > X0 > X0 > X0))).
% 0.90/0.49 thf(func_def_19, type, minus_minus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.90/0.49 thf(func_def_20, type, plus_plus: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.90/0.49 thf(func_def_21, type, uminus_uminus: !>[X0: $tType]:((X0 > X0))).
% 0.90/0.49 thf(func_def_22, type, locali1648044335f_frac: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > set @ X0 > $o))).
% 0.90/0.49 thf(func_def_23, type, locali7914339f_crng: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > set @ X0 > $o))).
% 0.90/0.49 thf(func_def_24, type, locali1402578320of_rng: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > set @ X0 > $o))).
% 0.90/0.49 thf(func_def_25, type, locali1441642228monoid: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ X1 > set @ X0 > $o))).
% 0.90/0.49 thf(func_def_26, type, bot_bot: !>[X0: $tType]:(X0)).
% 0.90/0.49 thf(func_def_27, type, ord_less_eq: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.90/0.49 thf(func_def_28, type, product_fst: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X0))).
% 0.90/0.49 thf(func_def_29, type, product_snd: !>[X0: $tType, X1: $tType]:((product_prod @ X0 @ X1 > X1))).
% 0.90/0.49 thf(func_def_30, type, a_inv: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > X0 > X0))).
% 0.90/0.49 thf(func_def_31, type, a_minus: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > X0 > X0 > X0))).
% 0.90/0.49 thf(func_def_32, type, add_pow: !>[X0: $tType, X1: $tType, X2: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > X2 > X0 > X0))).
% 0.90/0.49 thf(func_def_33, type, add: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > X0 > X0 > X0))).
% 0.90/0.49 thf(func_def_34, type, zero: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > X0))).
% 0.90/0.49 thf(func_def_35, type, semiring: !>[X0: $tType, X1: $tType]:((partia1265057091ct_ext @ X0 @ monoid_ext @ X0 @ ring_ext @ X0 @ X1 > $o))).
% 0.90/0.49 thf(func_def_36, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.90/0.49 thf(func_def_37, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.90/0.49 thf(func_def_38, type, r: partia1265057091ct_ext @ a @ monoid_ext @ a @ ring_ext @ a @ b).
% 0.90/0.49 thf(func_def_39, type, s: set @ a).
% 0.90/0.49 thf(func_def_40, type, r2: a).
% 0.90/0.49 thf(func_def_41, type, r3: a).
% 0.90/0.49 thf(func_def_42, type, s2: a).
% 0.90/0.49 thf(func_def_43, type, s3: a).
% 0.90/0.49 thf(func_def_44, type, t: a).
% 0.90/0.49 thf(func_def_45, type, t2: a).
% 0.90/0.49 thf(func_def_46, type, x: product_prod @ a @ a).
% 0.90/0.49 thf(func_def_47, type, y: product_prod @ a @ a).
% 0.90/0.49 thf(func_def_51, type, db1: !>[X0: $tType]:(X0)).
% 0.90/0.49 thf(func_def_52, type, db0: !>[X0: $tType]:(X0)).
% 0.90/0.49 thf(func_def_53, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.90/0.49 thf(func_def_54, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.90/0.49 thf(func_def_55, type, db2: !>[X0: $tType]:(X0)).
% 0.90/0.49 thf(func_def_56, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.90/0.49 thf(func_def_57, type, vAND: ($o > $o > $o)).
% 0.90/0.49 thf(func_def_58, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.90/0.49 thf(func_def_59, type, vIMP: ($o > $o > $o)).
% 0.90/0.49 thf(func_def_60, type, sK0: a).
% 0.90/0.49 thf(func_def_61, type, sK1: (set @ a > a)).
% 0.90/0.49 thf(func_def_62, type, sK2: (set @ a > a)).
% 0.90/0.49 thf(func_def_63, type, sK3: (set @ a > a)).
% 0.90/0.49 thf(func_def_64, type, sK4: (a > a)).
% 0.90/0.49 thf(func_def_65, type, sK5: !>[X0: $tType]:((set @ X0 > X0))).
% 0.90/0.49 thf(func_def_66, type, sK6: !>[X0: $tType]:((set @ X0 > X0))).
% 0.90/0.49 thf(func_def_67, type, sK7: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.90/0.49 thf(func_def_68, type, sK8: !>[X0: $tType]:((X0 > X0 > X0))).
% 0.90/0.49 thf(func_def_69, type, sK9: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.90/0.49 thf(func_def_70, type, sK10: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X0))).
% 0.90/0.49 thf(func_def_71, type, sK11: !>[X0: $tType, X1: $tType]:(((X0 > X1 > $o) > X1))).
% 0.90/0.49 thf(func_def_72, type, sK12: !>[X0: $tType]:((set @ X0 > X0))).
% 0.90/0.49 thf(func_def_73, type, sK13: a).
% 0.90/0.49 thf(func_def_74, type, sK14: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.90/0.49 thf(func_def_75, type, sK15: (a > a)).
% 0.90/0.49 thf(func_def_76, type, sK16: !>[X0: $tType]:((set @ X0 > set @ X0 > X0))).
% 0.90/0.49 thf(func_def_77, type, sK17: (a > a)).
% 0.90/0.49 thf(func_def_78, type, vNOT: ($o > $o)).
% 0.90/0.49 thf(f1,axiom,(
% 0.90/0.49 (member @ a @ t @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))),
% 0.90/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_f18)).
% 0.90/0.49 thf(f2,axiom,(
% 0.90/0.49 (member @ a @ t2 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))),
% 0.90/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_f17)).
% 0.90/0.49 thf(f13,axiom,(
% 0.90/0.49 (member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))),
% 0.90/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_f41)).
% 0.90/0.49 thf(f14,axiom,(
% 0.90/0.49 (member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))),
% 0.90/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_f42)).
% 0.90/0.49 thf(f20,axiom,(
% 0.90/0.49 (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (mult @ a @ ring_ext @ a @ b @ r @ t @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y))))))) = ((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))),
% 0.90/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_f40)).
% 0.90/0.49 thf(f22,axiom,(
% 0.90/0.49 (member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r)) => ((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r)) => ((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r)) => (((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))) = ((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))))),
% 0.90/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21__092_060open_062_092_060lbrakk_062snd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_A_092_060in_062_Acarrier_AR_059_Asnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_A_092_060in_062_Acarrier_AR_059_At_A_092_060otimes_062_At_H_A_092_060in_062_Acarrier_AR_092_060rbrakk_062_A_092_060Longrightarrow_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_A_092_060oplus_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_J_A_061_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ay_H_A_092_060otimes_062_Afst_Ax_H_J_J_A_092_060oplus_062_At_A_092_060otimes_062_At_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Asnd_Ay_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_A_Isnd_Ax_H_A_092_060otimes_062_Afst_Ay_H_J_J_092_060close_062)).
% 0.90/0.49 thf(f63,axiom,(
% 0.90/0.49 ! [X1 : a,X0 : a] : ((member @ a @ X0 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r)) => ((member @ a @ X1 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r)) => (member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ X0 @ X1) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))))),
% 0.90/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_semiring__simprules_I3_J)).
% 0.90/0.49 thf(f269,conjecture,(
% 0.90/0.49 (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (mult @ a @ ring_ext @ a @ b @ r @ t @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y))))))) = ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))),
% 0.90/0.49 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 0.90/0.49 thf(f270,negated_conjecture,(
% 0.90/0.49 ~ (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (mult @ a @ ring_ext @ a @ b @ r @ t @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y))))))) = ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))),
% 0.90/0.49 inference(negated_conjecture,[status(cth)],[f269])).
% 0.90/0.49 thf(f305,plain,(
% 0.90/0.49 (member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r)) => ((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r)) => ((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r)) => (((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))) = ((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))))),
% 0.90/0.49 inference(rectify,[],[f22])).
% 0.90/0.49 thf(f306,plain,(
% 0.90/0.49 (((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true) => ((((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true) => ((((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true) => (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))) = ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))))),
% 0.90/0.49 inference(fool_elimination,[],[f305])).
% 0.90/0.49 thf(f311,plain,(
% 0.90/0.49 (member @ a @ t2 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))),
% 0.90/0.49 inference(rectify,[],[f2])).
% 0.90/0.49 thf(f312,plain,(
% 0.90/0.49 (((member @ a @ t2 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)),
% 0.90/0.49 inference(fool_elimination,[],[f311])).
% 0.90/0.49 thf(f349,plain,(
% 0.90/0.49 ! [X0 : a,X1 : a] : ((member @ a @ X1 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r)) => ((member @ a @ X0 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r)) => (member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ X1 @ X0) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))))),
% 0.90/0.49 inference(rectify,[],[f63])).
% 0.90/0.49 thf(f350,plain,(
% 0.90/0.49 ! [X1 : a,X0 : a] : ((((member @ a @ X1 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true) => ((((member @ a @ X0 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true) => (((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ X1 @ X0) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)))),
% 0.90/0.49 inference(fool_elimination,[],[f349])).
% 0.90/0.49 thf(f467,plain,(
% 0.90/0.49 (member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))),
% 0.90/0.49 inference(rectify,[],[f13])).
% 0.90/0.49 thf(f468,plain,(
% 0.90/0.49 (((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)),
% 0.90/0.49 inference(fool_elimination,[],[f467])).
% 0.90/0.49 thf(f511,plain,(
% 0.90/0.49 (member @ a @ t @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))),
% 0.90/0.49 inference(rectify,[],[f1])).
% 0.90/0.49 thf(f512,plain,(
% 0.90/0.49 (((member @ a @ t @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)),
% 0.90/0.49 inference(fool_elimination,[],[f511])).
% 0.90/0.49 thf(f679,plain,(
% 0.90/0.49 (member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))),
% 0.90/0.49 inference(rectify,[],[f14])).
% 0.90/0.49 thf(f680,plain,(
% 0.90/0.49 (((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)),
% 0.90/0.49 inference(fool_elimination,[],[f679])).
% 0.90/0.49 thf(f737,plain,(
% 0.90/0.49 (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (mult @ a @ ring_ext @ a @ b @ r @ t @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y))))))) != ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))),
% 0.90/0.49 inference(flattening,[],[f270])).
% 0.90/0.49 thf(f765,plain,(
% 0.90/0.49 (((((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))) = ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))))) | (((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true)) | (((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true)) | (((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true)),
% 0.90/0.49 inference(ennf_transformation,[],[f306])).
% 0.90/0.49 thf(f766,plain,(
% 0.90/0.49 (((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true) | (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))) = ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))))) | (((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true) | (((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true)),
% 0.90/0.49 inference(flattening,[],[f765])).
% 0.90/0.49 thf(f820,plain,(
% 0.90/0.49 ! [X1 : a,X0 : a] : (((((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ X1 @ X0) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true) | (((member @ a @ X0 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true)) | (((member @ a @ X1 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true))),
% 0.90/0.49 inference(ennf_transformation,[],[f350])).
% 0.90/0.49 thf(f821,plain,(
% 0.90/0.49 ! [X1 : a,X0 : a] : ((((member @ a @ X1 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true) | (((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ X1 @ X0) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true) | (((member @ a @ X0 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true))),
% 0.90/0.49 inference(flattening,[],[f820])).
% 0.90/0.49 thf(f1126,plain,(
% 0.90/0.49 ! [X0 : a,X1 : a] : ((((member @ a @ X0 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true) | (((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ X0 @ X1) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true) | (((member @ a @ X1 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true))),
% 0.90/0.49 inference(rectify,[],[f821])).
% 0.90/0.49 thf(f1245,plain,(
% 0.90/0.49 (((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true) | (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))) = ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))))) | (((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true) | (((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true)),
% 0.90/0.49 inference(cnf_transformation,[],[f766])).
% 0.90/0.49 thf(f1273,plain,(
% 0.90/0.49 (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (mult @ a @ ring_ext @ a @ b @ r @ t @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y))))))) != ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))),
% 0.90/0.49 inference(cnf_transformation,[],[f737])).
% 0.90/0.49 thf(f1285,plain,(
% 0.90/0.49 (((member @ a @ t2 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)),
% 0.90/0.49 inference(cnf_transformation,[],[f312])).
% 0.90/0.49 thf(f1392,plain,(
% 0.90/0.49 ( ! [X0 : a,X1 : a] : ((((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ X0 @ X1) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true) | (((member @ a @ X0 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true) | (((member @ a @ X1 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true)) )),
% 0.90/0.49 inference(cnf_transformation,[],[f1126])).
% 0.90/0.49 thf(f1394,plain,(
% 0.90/0.49 (((member @ a @ t @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)),
% 0.90/0.49 inference(cnf_transformation,[],[f512])).
% 0.90/0.49 thf(f1405,plain,(
% 0.90/0.49 (((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)),
% 0.90/0.49 inference(cnf_transformation,[],[f468])).
% 0.90/0.49 thf(f1419,plain,(
% 0.90/0.49 (((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)),
% 0.90/0.49 inference(cnf_transformation,[],[f680])).
% 0.90/0.49 thf(f1438,plain,(
% 0.90/0.49 (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (mult @ a @ ring_ext @ a @ b @ r @ t @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y))))))) = ((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))),
% 0.90/0.49 inference(cnf_transformation,[],[f20])).
% 0.90/0.49 thf(f1581,definition,(
% 0.90/0.49 spl18_5 <=> (((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)),
% 0.90/0.49 introduced(definition,[new_symbols(definition,[spl18_5])],[avatar_definition])).
% 0.90/0.49 thf(f1584,plain,(
% 0.90/0.49 spl18_5),
% 0.90/0.49 inference(avatar_split_clause,[],[f1419,f1581])).
% 0.90/0.49 thf(f1636,definition,(
% 0.90/0.49 spl18_16 <=> (((member @ a @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)),
% 0.90/0.49 introduced(definition,[new_symbols(definition,[spl18_16])],[avatar_definition])).
% 0.90/0.49 thf(f1639,plain,(
% 0.90/0.49 spl18_16),
% 0.90/0.49 inference(avatar_split_clause,[],[f1405,f1636])).
% 0.90/0.49 thf(f1724,definition,(
% 0.90/0.49 spl18_34 <=> (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (mult @ a @ ring_ext @ a @ b @ r @ t @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y))))))) = ((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))),
% 0.90/0.49 introduced(definition,[new_symbols(definition,[spl18_34])],[avatar_definition])).
% 0.90/0.49 thf(f1727,plain,(
% 0.90/0.49 spl18_34),
% 0.90/0.49 inference(avatar_split_clause,[],[f1438,f1724])).
% 0.90/0.49 thf(f1735,definition,(
% 0.90/0.49 spl18_36 <=> (((member @ a @ t2 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)),
% 0.90/0.49 introduced(definition,[new_symbols(definition,[spl18_36])],[avatar_definition])).
% 0.90/0.49 thf(f1737,plain,(
% 0.90/0.49 (((member @ a @ t2 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true) | ~spl18_36),
% 0.90/0.49 inference(avatar_component_clause,[],[f1735])).
% 0.90/0.49 thf(f1738,plain,(
% 0.90/0.49 spl18_36),
% 0.90/0.49 inference(avatar_split_clause,[],[f1285,f1735])).
% 0.90/0.49 thf(f1745,definition,(
% 0.90/0.49 spl18_38 <=> (((member @ a @ t @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)),
% 0.90/0.49 introduced(definition,[new_symbols(definition,[spl18_38])],[avatar_definition])).
% 0.90/0.49 thf(f1747,plain,(
% 0.90/0.49 (((member @ a @ t @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true) | ~spl18_38),
% 0.90/0.49 inference(avatar_component_clause,[],[f1745])).
% 0.90/0.49 thf(f1748,plain,(
% 0.90/0.49 spl18_38),
% 0.90/0.49 inference(avatar_split_clause,[],[f1394,f1745])).
% 0.90/0.49 thf(f1806,definition,(
% 0.90/0.49 spl18_50 <=> (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (mult @ a @ ring_ext @ a @ b @ r @ t @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y))))))) = ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))),
% 0.90/0.49 introduced(definition,[new_symbols(definition,[spl18_50])],[avatar_definition])).
% 0.90/0.49 thf(f1809,plain,(
% 0.90/0.49 ~spl18_50),
% 0.90/0.49 inference(avatar_split_clause,[],[f1273,f1806])).
% 0.90/0.49 thf(f1882,definition,(
% 0.90/0.49 spl18_65 <=> (((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) = $true)),
% 0.90/0.49 introduced(definition,[new_symbols(definition,[spl18_65])],[avatar_definition])).
% 0.90/0.49 thf(f1884,plain,(
% 0.90/0.49 (((member @ a @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true) | spl18_65),
% 0.90/0.49 inference(avatar_component_clause,[],[f1882])).
% 0.90/0.49 thf(f1886,definition,(
% 0.90/0.49 spl18_66 <=> (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))) = ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))),
% 0.90/0.49 introduced(definition,[new_symbols(definition,[spl18_66])],[avatar_definition])).
% 0.90/0.49 thf(f1889,plain,(
% 0.90/0.49 ~spl18_65 | ~spl18_5 | spl18_66 | ~spl18_16),
% 0.90/0.49 inference(avatar_split_clause,[],[f1245,f1636,f1886,f1581,f1882])).
% 0.90/0.49 thf(f2094,plain,(
% 0.90/0.49 (((member @ a @ t @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true) | (((member @ a @ t2 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true) | ($true != $true) | spl18_65),
% 0.90/0.49 inference(superposition,[],[f1884,f1392])).
% 0.90/0.49 thf(f2097,plain,(
% 0.90/0.49 (((member @ a @ t @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true) | (((member @ a @ t2 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true) | spl18_65),
% 0.90/0.49 inference(trivial_inequality_removal,[],[f2094])).
% 0.90/0.49 thf(f2098,plain,(
% 0.90/0.49 (((member @ a @ t2 @ (partial_carrier @ a @ monoid_ext @ a @ ring_ext @ a @ b @ r))) != $true) | (~spl18_38 | spl18_65)),
% 0.90/0.49 inference(forward_subsumption_resolution,[],[f2097,f1747])).
% 0.90/0.49 thf(f2099,plain,(
% 0.90/0.49 $false | (~spl18_36 | ~spl18_38 | spl18_65)),
% 0.90/0.49 inference(forward_subsumption_resolution,[],[f2098,f1737])).
% 0.90/0.49 thf(f2100,plain,(
% 0.90/0.49 ~spl18_36 | ~spl18_38 | spl18_65),
% 0.90/0.49 inference(avatar_contradiction_clause,[],[f2099])).
% 0.90/0.49 thf(f2101,definition,(
% 0.90/0.49 (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (mult @ a @ ring_ext @ a @ b @ r @ t @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y))))))) != ((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))))) | (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))) != ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y)))))))) | (((add @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t @ s3) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ r2) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ (product_fst @ a @ a @ x))))) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ s2) @ (product_snd @ a @ a @ x)) @ (mult @ a @ ring_ext @ a @ b @ r @ t @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ r3) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ (product_fst @ a @ a @ y))))))) = ((mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ t2 @ t) @ (add @ a @ b @ r @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s3 @ r2)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ y) @ (product_fst @ a @ a @ x)))) @ (a_minus @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_snd @ a @ a @ y)) @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ r3)) @ (mult @ a @ ring_ext @ a @ b @ r @ (mult @ a @ ring_ext @ a @ b @ r @ s2 @ s3) @ (mult @ a @ ring_ext @ a @ b @ r @ (product_snd @ a @ a @ x) @ (product_fst @ a @ a @ y))))))))),
% 0.90/0.49 introduced(theory,[theory_tautology_sat_conflict])).
% 0.90/0.49 cnf(s5, plain, spl18_5, inference(sat_conversion,[],[f1584])).
% 0.90/0.49 cnf(s16, plain, spl18_16, inference(sat_conversion,[],[f1639])).
% 0.90/0.49 cnf(s33, plain, spl18_34, inference(sat_conversion,[],[f1727])).
% 0.90/0.49 cnf(s36, plain, spl18_36, inference(sat_conversion,[],[f1738])).
% 0.90/0.49 cnf(s38, plain, spl18_38, inference(sat_conversion,[],[f1748])).
% 0.90/0.49 cnf(s51, plain, ~spl18_50, inference(sat_conversion,[],[f1809])).
% 0.90/0.49 cnf(s67, plain, ~spl18_5 | ~spl18_16 | ~spl18_65 | spl18_66, inference(sat_conversion,[],[f1889])).
% 0.90/0.49 cnf(s104, plain, ~spl18_36 | ~spl18_38 | spl18_65, inference(sat_conversion,[],[f2100])).
% 0.90/0.49 cnf(s105, plain, ~spl18_34 | spl18_50 | ~spl18_66, inference(sat_conversion,[],[f2101])).
% 0.90/0.49 cnf(s110, plain, spl18_65, inference(rat,[],[s104,s38,s36])).
% 0.90/0.49 cnf(s113, plain, ~spl18_66, inference(rat,[],[s105,s51,s33])).
% 0.90/0.49 cnf(s114, plain, ~spl18_5, inference(rat,[],[s67,s113,s110,s16])).
% 0.90/0.49 cnf(s119, plain, $false, inference(rat,[],[s5,s114])).
% 0.90/0.49 thf(f2102,plain,(
% 0.90/0.49 $false),
% 0.90/0.49 inference(avatar_sat_refutation,[],[s119])).
% 0.90/0.49 % SZS output end Proof for theBenchmark
% 0.90/0.49 % (562288)------------------------------
% 0.90/0.49 % (562288)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.90/0.49 % (562288)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.90/0.49 % (562288)CaDiCaL version: 2.1.3
% 0.90/0.49 % (562288)Termination reason: Refutation
% 0.90/0.49 % (562288)Time elapsed: 0.106 s
% 0.90/0.49 % (562288)Peak memory usage: 14 MB
% 0.90/0.49 % (562288)Instructions burned: 244 (million)
% 0.90/0.49 % (562280)Success in time 0.178 s
% 0.90/0.49 % Vampire exiting
%------------------------------------------------------------------------------