%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP095^1 : 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 : n009.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 08:08:19 AM UTC 2026
% Result : Theorem 1.38s 0.48s
% Output : Refutation 1.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP095^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n009.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 19:53:00 UTC 2026
% 0.07/0.17 % CPUTime :
% 0.07/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 Running higher-order theorem proving
% 0.07/0.25 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
% 0.71/0.39 % (272496)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.71/0.39 % (272501)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3721587889:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.71/0.39 % (272507)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.71/0.39 % (272507)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
% 0.71/0.39 % (272502)lrs+10_16_si=on:nwc=1.5:random_seed=3015274546:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.71/0.39 % (272503)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2299868948:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.71/0.39 % (272505)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2104641832:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.71/0.39 % (272504)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=3773810194: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)
% 0.71/0.39 % (272506)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2098413726:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.71/0.39 % (272507)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=2594121160:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.71/0.39 % (272503)Instruction limit reached!
% 0.71/0.39 % (272503)------------------------------
% 0.71/0.39 % (272503)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.39 % (272503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.39 % (272503)CaDiCaL version: 2.1.3
% 0.71/0.39 % (272503)Termination reason: Instruction limit
% 0.71/0.39 % (272503)Termination phase: shuffling
% 0.71/0.39 % (272503)Time elapsed: 0.003 s
% 0.71/0.39 % (272503)Peak memory usage: 10 MB
% 0.71/0.39 % (272503)Instructions burned: 6 (million)
% 0.71/0.39 % (272502)Instruction limit reached!
% 0.71/0.39 % (272502)------------------------------
% 0.71/0.39 % (272502)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.39 % (272502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.39 % (272502)CaDiCaL version: 2.1.3
% 0.71/0.39 % (272502)Termination reason: Instruction limit
% 0.71/0.39 % (272502)Termination phase: Property scanning
% 0.71/0.39 % (272502)Time elapsed: 0.008 s
% 0.71/0.39 % (272502)Peak memory usage: 10 MB
% 0.71/0.39 % (272502)Instructions burned: 19 (million)
% 0.71/0.39 % (272505)Instruction limit reached!
% 0.71/0.39 % (272505)------------------------------
% 0.71/0.39 % (272505)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.39 % (272505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.39 % (272505)CaDiCaL version: 2.1.3
% 0.71/0.39 % (272505)Termination reason: Instruction limit
% 0.71/0.39 % (272505)Termination phase: Property scanning
% 0.71/0.39 % (272505)Time elapsed: 0.011 s
% 0.71/0.39 % (272505)Peak memory usage: 10 MB
% 0.71/0.39 % (272505)Instructions burned: 26 (million)
% 0.71/0.39 % (272501)Instruction limit reached!
% 0.71/0.39 % (272501)------------------------------
% 0.71/0.39 % (272501)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.39 % (272501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.39 % (272501)CaDiCaL version: 2.1.3
% 0.71/0.39 % (272501)Termination reason: Instruction limit
% 0.71/0.39 % (272501)Termination phase: Saturation
% 0.71/0.39 % (272501)Time elapsed: 0.021 s
% 0.71/0.39 % (272501)Peak memory usage: 12 MB
% 0.71/0.39 % (272501)Instructions burned: 91 (million)
% 0.71/0.39 % (272515)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3724407197:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.71/0.39 % (272518)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2321698101:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.71/0.39 % (272515)Instruction limit reached!
% 0.71/0.42 % (272515)------------------------------
% 0.71/0.42 % (272515)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.42 % (272515)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.42 % (272515)CaDiCaL version: 2.1.3
% 0.71/0.42 % (272515)Termination reason: Instruction limit
% 0.71/0.42 % (272515)Termination phase: shuffling
% 0.71/0.42 % (272515)Time elapsed: 0.003 s
% 0.71/0.42 % (272515)Peak memory usage: 10 MB
% 0.71/0.42 % (272515)Instructions burned: 6 (million)
% 0.71/0.42 % (272517)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.71/0.42 % (272518)Instruction limit reached!
% 0.71/0.42 % (272518)------------------------------
% 0.71/0.42 % (272518)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.42 % (272518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.42 % (272518)CaDiCaL version: 2.1.3
% 0.71/0.42 % (272518)Termination reason: Instruction limit
% 0.71/0.42 % (272518)Termination phase: shuffling
% 0.71/0.42 % (272518)Time elapsed: 0.003 s
% 0.71/0.42 % (272518)Peak memory usage: 10 MB
% 0.71/0.42 % (272518)Instructions burned: 13 (million)
% 0.71/0.42 % (272517)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3332452050:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.71/0.42 % (272506)Instruction limit reached!
% 0.71/0.42 % (272506)------------------------------
% 0.71/0.42 % (272506)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.42 % (272506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.42 % (272506)CaDiCaL version: 2.1.3
% 0.71/0.42 % (272506)Termination reason: Instruction limit
% 0.71/0.42 % (272506)Termination phase: Property scanning
% 0.71/0.42 % (272506)Time elapsed: 0.033 s
% 0.71/0.42 % (272506)Peak memory usage: 12 MB
% 0.71/0.42 % (272506)Instructions burned: 75 (million)
% 0.71/0.42 % (272517)Instruction limit reached!
% 0.71/0.42 % (272517)------------------------------
% 0.71/0.42 % (272517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.42 % (272517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.42 % (272517)CaDiCaL version: 2.1.3
% 0.71/0.42 % (272517)Termination reason: Instruction limit
% 0.71/0.42 % (272517)Termination phase: shuffling
% 0.71/0.42 % (272517)Time elapsed: 0.004 s
% 0.71/0.42 % (272517)Peak memory usage: 10 MB
% 0.71/0.42 % (272517)Instructions burned: 8 (million)
% 0.71/0.42 % (272516)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1255758823:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.71/0.42 % (272522)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=1649574059:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.71/0.42 % (272516)Instruction limit reached!
% 0.71/0.42 % (272516)------------------------------
% 0.71/0.42 % (272516)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.42 % (272516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.42 % (272516)CaDiCaL version: 2.1.3
% 0.71/0.42 % (272516)Termination reason: Instruction limit
% 0.71/0.42 % (272516)Termination phase: shuffling
% 0.71/0.42 % (272516)Time elapsed: 0.003 s
% 0.71/0.42 % (272516)Peak memory usage: 10 MB
% 0.71/0.42 % (272516)Instructions burned: 7 (million)
% 0.71/0.42 % (272521)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
% 0.71/0.42 % (272521)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.71/0.42 % (272521)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3027692714:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.71/0.42 % (272525)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.71/0.42 % (272525)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=3409132909:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.71/0.44 % (272525)Instruction limit reached!
% 0.71/0.44 % (272525)------------------------------
% 0.71/0.44 % (272525)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.44 % (272525)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.44 % (272525)CaDiCaL version: 2.1.3
% 0.71/0.44 % (272525)Termination reason: Instruction limit
% 0.71/0.44 % (272525)Termination phase: shuffling
% 0.71/0.44 % (272525)Time elapsed: 0.003 s
% 0.71/0.44 % (272525)Peak memory usage: 10 MB
% 0.71/0.44 % (272525)Instructions burned: 6 (million)
% 0.71/0.44 % (272522)Instruction limit reached!
% 0.71/0.44 % (272522)------------------------------
% 0.71/0.44 % (272522)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.44 % (272522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.44 % (272522)CaDiCaL version: 2.1.3
% 0.71/0.44 % (272522)Termination reason: Instruction limit
% 0.71/0.44 % (272522)Termination phase: Function definition elimination
% 0.71/0.44 % (272522)Time elapsed: 0.019 s
% 0.71/0.44 % (272522)Peak memory usage: 11 MB
% 0.71/0.44 % (272522)Instructions burned: 91 (million)
% 0.71/0.44 % (272521)Instruction limit reached!
% 0.71/0.44 % (272521)------------------------------
% 0.71/0.44 % (272521)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.44 % (272521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.44 % (272521)CaDiCaL version: 2.1.3
% 0.71/0.44 % (272521)Termination reason: Instruction limit
% 0.71/0.44 % (272521)Termination phase: shuffling
% 0.71/0.44 % (272521)Time elapsed: 0.013 s
% 0.71/0.44 % (272521)Peak memory usage: 10 MB
% 0.71/0.44 % (272521)Instructions burned: 29 (million)
% 0.71/0.44 % (272524)lrs+10_1_si=on:cs=on:random_seed=2906927892:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.71/0.44 % (272531)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1047420375:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.71/0.44 % (272524)Instruction limit reached!
% 0.71/0.44 % (272524)------------------------------
% 0.71/0.44 % (272524)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.44 % (272524)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.44 % (272524)CaDiCaL version: 2.1.3
% 0.71/0.44 % (272524)Termination reason: Instruction limit
% 0.71/0.44 % (272524)Termination phase: shuffling
% 0.71/0.44 % (272524)Time elapsed: 0.011 s
% 0.71/0.44 % (272524)Peak memory usage: 10 MB
% 0.71/0.44 % (272524)Instructions burned: 9 (million)
% 0.71/0.44 % (272528)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3723157627:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.71/0.44 % (272532)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1914222680:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.71/0.44 % (272533)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2503779209:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.71/0.44 % (272507)Instruction limit reached!
% 0.71/0.44 % (272507)------------------------------
% 0.71/0.44 % (272507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.44 % (272507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.44 % (272507)CaDiCaL version: 2.1.3
% 0.71/0.44 % (272507)Termination reason: Instruction limit
% 0.71/0.44 % (272507)Termination phase: Saturation
% 0.71/0.44 % (272507)Time elapsed: 0.076 s
% 0.71/0.44 % (272507)Peak memory usage: 13 MB
% 0.71/0.44 % (272507)Instructions burned: 158 (million)
% 0.71/0.44 % (272533)Instruction limit reached!
% 0.71/0.44 % (272533)------------------------------
% 0.71/0.44 % (272533)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.71/0.44 % (272533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.71/0.44 % (272533)CaDiCaL version: 2.1.3
% 0.71/0.44 % (272533)Termination reason: Instruction limit
% 0.71/0.44 % (272533)Termination phase: shuffling
% 0.71/0.44 % (272533)Time elapsed: 0.006 s
% 0.71/0.44 % (272533)Peak memory usage: 10 MB
% 0.71/0.44 % (272533)Instructions burned: 14 (million)
% 0.71/0.44 % (272531)Refutation not found, incomplete strategy
% 1.38/0.48 % (272531)------------------------------
% 1.38/0.48 % (272531)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.48 % (272531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.48 % (272531)CaDiCaL version: 2.1.3
% 1.38/0.48 % (272531)Termination reason: Refutation not found, incomplete strategy
% 1.38/0.48 % (272531)Time elapsed: 0.019 s
% 1.38/0.48 % (272531)Peak memory usage: 13 MB
% 1.38/0.48 % (272531)Instructions burned: 74 (million)
% 1.38/0.48 % (272531)------------------------------
% 1.38/0.48 % (272531)------------------------------
% 1.38/0.48 % (272532)Instruction limit reached!
% 1.38/0.48 % (272532)------------------------------
% 1.38/0.48 % (272532)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.48 % (272532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.48 % (272532)CaDiCaL version: 2.1.3
% 1.38/0.48 % (272532)Termination reason: Instruction limit
% 1.38/0.48 % (272532)Termination phase: Property scanning
% 1.38/0.48 % (272532)Time elapsed: 0.011 s
% 1.38/0.48 % (272532)Peak memory usage: 10 MB
% 1.38/0.48 % (272532)Instructions burned: 26 (million)
% 1.38/0.48 % (272528)Instruction limit reached!
% 1.38/0.48 % (272528)------------------------------
% 1.38/0.48 % (272528)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.48 % (272528)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.48 % (272528)CaDiCaL version: 2.1.3
% 1.38/0.48 % (272528)Termination reason: Instruction limit
% 1.38/0.48 % (272528)Termination phase: Preprocessing 3
% 1.38/0.48 % (272528)Time elapsed: 0.018 s
% 1.38/0.48 % (272528)Peak memory usage: 11 MB
% 1.38/0.48 % (272528)Instructions burned: 39 (million)
% 1.38/0.48 % (272537)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3529907072:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.38/0.48 % (272540)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3183358539:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.38/0.48 % (272542)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=435652321:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.38/0.48 % (272541)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2048351169: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)
% 1.38/0.48 % (272540)Instruction limit reached!
% 1.38/0.48 % (272540)------------------------------
% 1.38/0.48 % (272540)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.48 % (272540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.48 % (272540)CaDiCaL version: 2.1.3
% 1.38/0.48 % (272540)Termination reason: Instruction limit
% 1.38/0.48 % (272540)Termination phase: shuffling
% 1.38/0.48 % (272540)Time elapsed: 0.006 s
% 1.38/0.48 % (272540)Peak memory usage: 10 MB
% 1.38/0.48 % (272540)Instructions burned: 14 (million)
% 1.38/0.48 % (272541)Instruction limit reached!
% 1.38/0.48 % (272541)------------------------------
% 1.38/0.48 % (272541)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.48 % (272541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.48 % (272541)CaDiCaL version: 2.1.3
% 1.38/0.48 % (272541)Termination reason: Instruction limit
% 1.38/0.48 % (272541)Termination phase: shuffling
% 1.38/0.48 % (272541)Time elapsed: 0.003 s
% 1.38/0.48 % (272541)Peak memory usage: 10 MB
% 1.38/0.48 % (272541)Instructions burned: 5 (million)
% 1.38/0.48 % (272542)Instruction limit reached!
% 1.38/0.48 % (272542)------------------------------
% 1.38/0.48 % (272542)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.48 % (272542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.48 % (272542)CaDiCaL version: 2.1.3
% 1.38/0.48 % (272542)Termination reason: Instruction limit
% 1.38/0.48 % (272542)Termination phase: shuffling
% 1.38/0.48 % (272542)Time elapsed: 0.007 s
% 1.38/0.48 % (272542)Peak memory usage: 10 MB
% 1.38/0.48 % (272542)Instructions burned: 29 (million)
% 1.38/0.48 % (272543)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1843111202:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.38/0.48 % (272545)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=4209843855:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.38/0.48 % (272551)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=828794918:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.38/0.48 % (272549)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
% 1.38/0.48 % (272549)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.38/0.48 % (272543)Instruction limit reached!
% 1.38/0.48 % (272543)------------------------------
% 1.38/0.48 % (272543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.48 % (272543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.48 % (272543)CaDiCaL version: 2.1.3
% 1.38/0.48 % (272543)Termination reason: Instruction limit
% 1.38/0.48 % (272543)Termination phase: Property scanning
% 1.38/0.48 % (272543)Time elapsed: 0.011 s
% 1.38/0.48 % (272543)Peak memory usage: 10 MB
% 1.38/0.48 % (272543)Instructions burned: 25 (million)
% 1.38/0.48 % (272550)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.38/0.48 % (272549)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=1590102425:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.38/0.48 % (272551)Instruction limit reached!
% 1.38/0.48 % (272551)------------------------------
% 1.38/0.48 % (272551)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.48 % (272551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.48 % (272551)CaDiCaL version: 2.1.3
% 1.38/0.48 % (272551)Termination reason: Instruction limit
% 1.38/0.48 % (272551)Termination phase: Property scanning
% 1.38/0.48 % (272551)Time elapsed: 0.007 s
% 1.38/0.48 % (272551)Peak memory usage: 10 MB
% 1.38/0.48 % (272551)Instructions burned: 33 (million)
% 1.38/0.48 % (272550)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=1737516441:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.38/0.48 % (272550)Instruction limit reached!
% 1.38/0.48 % (272550)------------------------------
% 1.38/0.48 % (272550)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.48 % (272550)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.48 % (272550)CaDiCaL version: 2.1.3
% 1.38/0.48 % (272550)Termination reason: Instruction limit
% 1.38/0.48 % (272550)Termination phase: shuffling
% 1.38/0.48 % (272550)Time elapsed: 0.004 s
% 1.38/0.48 % (272550)Peak memory usage: 10 MB
% 1.38/0.48 % (272550)Instructions burned: 9 (million)
% 1.38/0.48 % (272549)Instruction limit reached!
% 1.38/0.48 % (272549)------------------------------
% 1.38/0.48 % (272549)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.48 % (272549)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.48 % (272549)CaDiCaL version: 2.1.3
% 1.38/0.48 % (272549)Termination reason: Instruction limit
% 1.38/0.48 % (272549)Termination phase: shuffling
% 1.38/0.48 % (272549)Time elapsed: 0.007 s
% 1.38/0.48 % (272549)Peak memory usage: 10 MB
% 1.38/0.48 % (272549)Instructions burned: 16 (million)
% 1.38/0.48 % (272558)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3139457362:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.38/0.48 % (272555)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=712925996:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.38/0.48 % (272558)Instruction limit reached!
% 1.38/0.48 % (272558)------------------------------
% 1.38/0.48 % (272558)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.48 % (272558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.48 % (272558)CaDiCaL version: 2.1.3
% 1.38/0.48 % (272558)Termination reason: Instruction limit
% 1.38/0.48 % (272558)Termination phase: shuffling
% 1.38/0.48 % (272558)Time elapsed: 0.005 s
% 1.38/0.48 % (272558)Peak memory usage: 10 MB
% 1.38/0.48 % (272558)Instructions burned: 23 (million)
% 1.38/0.48 % (272555)Instruction limit reached!
% 1.38/0.48 % (272555)------------------------------
% 1.38/0.48 % (272555)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.48 % (272555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.48 % (272555)CaDiCaL version: 2.1.3
% 1.38/0.48 % (272555)Termination reason: Instruction limit
% 1.38/0.48 % (272555)Termination phase: shuffling
% 1.38/0.48 % (272555)Time elapsed: 0.003 s
% 1.38/0.48 % (272555)Peak memory usage: 10 MB
% 1.38/0.48 % (272555)Instructions burned: 7 (million)
% 1.38/0.48 % (272559)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=138722345:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 1.38/0.48 % (272560)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2446709293:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.38/0.48 % (272545)Instruction limit reached!
% 1.38/0.48 % (272545)------------------------------
% 1.38/0.48 % (272545)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.48 % (272545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.48 % (272545)CaDiCaL version: 2.1.3
% 1.38/0.48 % (272545)Termination reason: Instruction limit
% 1.38/0.48 % (272545)Termination phase: Property scanning
% 1.38/0.48 % (272545)Time elapsed: 0.035 s
% 1.38/0.48 % (272545)Peak memory usage: 11 MB
% 1.38/0.48 % (272545)Instructions burned: 61 (million)
% 1.38/0.48 % (272563)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=324885257:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 1.38/0.48 % (272559)Instruction limit reached!
% 1.38/0.48 % (272559)------------------------------
% 1.38/0.48 % (272559)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.48 % (272559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.48 % (272559)CaDiCaL version: 2.1.3
% 1.38/0.48 % (272559)Termination reason: Instruction limit
% 1.38/0.48 % (272559)Termination phase: Property scanning
% 1.38/0.48 % (272559)Time elapsed: 0.009 s
% 1.38/0.48 % (272559)Peak memory usage: 10 MB
% 1.38/0.48 % (272559)Instructions burned: 21 (million)
% 1.38/0.48 % (272564)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=3731451617:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 1.38/0.48 % (272504) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-272496-272504"...
% 1.38/0.48 % (272504)...printing done.
% 1.38/0.48 % (272569)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.38/0.48 % (272504)Refutation found. Thanks to Tanya!
% 1.38/0.48 % SZS status Theorem for theBenchmark
% 1.38/0.48 % SZS output start Proof for theBenchmark
% 1.38/0.48 thf(type_def_5, type, poly_poly_real: $tType).
% 1.38/0.48 thf(type_def_6, type, set_poly_real: $tType).
% 1.38/0.48 thf(type_def_7, type, poly_real: $tType).
% 1.38/0.48 thf(type_def_8, type, poly_nat: $tType).
% 1.38/0.48 thf(type_def_9, type, poly_int: $tType).
% 1.38/0.48 thf(type_def_10, type, set_real: $tType).
% 1.38/0.48 thf(type_def_11, type, set_int: $tType).
% 1.38/0.48 thf(type_def_12, type, real: $tType).
% 1.38/0.48 thf(type_def_13, type, nat: $tType).
% 1.38/0.48 thf(type_def_14, type, int: $tType).
% 1.38/0.48 thf(type_def_15, type, sTfun: ($tType * $tType) > $tType).
% 1.38/0.48 thf(func_def_0, type, abs_abs_int: (int > int)).
% 1.38/0.48 thf(func_def_1, type, abs_abs_poly_real: (poly_real > poly_real)).
% 1.38/0.48 thf(func_def_2, type, abs_abs_real: (real > real)).
% 1.38/0.48 thf(func_def_3, type, minus_minus_real: (real > real > real)).
% 1.38/0.48 thf(func_def_4, type, one_one_int: int).
% 1.38/0.48 thf(func_def_5, type, one_one_nat: nat).
% 1.38/0.48 thf(func_def_6, type, one_one_poly_int: poly_int).
% 1.38/0.48 thf(func_def_7, type, one_one_poly_nat: poly_nat).
% 1.38/0.48 thf(func_def_8, type, one_one_poly_real: poly_real).
% 1.38/0.48 thf(func_def_9, type, one_one_real: real).
% 1.38/0.48 thf(func_def_10, type, zero_zero_int: int).
% 1.38/0.48 thf(func_def_11, type, zero_zero_nat: nat).
% 1.38/0.48 thf(func_def_12, type, zero_zero_poly_int: poly_int).
% 1.38/0.48 thf(func_def_13, type, zero_zero_poly_nat: poly_nat).
% 1.38/0.48 thf(func_def_14, type, zero_z1423781445y_real: poly_poly_real).
% 1.38/0.48 thf(func_def_15, type, zero_zero_poly_real: poly_real).
% 1.38/0.48 thf(func_def_16, type, zero_zero_real: real).
% 1.38/0.48 thf(func_def_17, type, ring_1_Ints_int: set_int).
% 1.38/0.48 thf(func_def_18, type, ring_1690226883y_real: set_poly_real).
% 1.38/0.48 thf(func_def_19, type, ring_1_Ints_real: set_real).
% 1.38/0.48 thf(func_def_20, type, ring_1_of_int_int: (int > int)).
% 1.38/0.48 thf(func_def_21, type, ring_12102921859ly_int: (int > poly_int)).
% 1.38/0.48 thf(func_def_22, type, ring_11511526659y_real: (int > poly_real)).
% 1.38/0.48 thf(func_def_23, type, ring_1_of_int_real: (int > real)).
% 1.38/0.48 thf(func_def_24, type, ord_less_int: (int > int > $o)).
% 1.38/0.48 thf(func_def_25, type, ord_less_nat: (nat > nat > $o)).
% 1.38/0.48 thf(func_def_26, type, ord_less_poly_real: (poly_real > poly_real > $o)).
% 1.38/0.48 thf(func_def_27, type, ord_less_real: (real > real > $o)).
% 1.38/0.48 thf(func_def_28, type, ord_less_eq_int: (int > int > $o)).
% 1.38/0.48 thf(func_def_29, type, ord_less_eq_nat: (nat > nat > $o)).
% 1.38/0.48 thf(func_def_30, type, ord_le1180086932y_real: (poly_real > poly_real > $o)).
% 1.38/0.48 thf(func_def_31, type, ord_less_eq_real: (real > real > $o)).
% 1.38/0.48 thf(func_def_32, type, algebraic_real: (real > $o)).
% 1.38/0.48 thf(func_def_33, type, degree_int: (poly_int > nat)).
% 1.38/0.48 thf(func_def_34, type, degree_nat: (poly_nat > nat)).
% 1.38/0.48 thf(func_def_35, type, degree_poly_real: (poly_poly_real > nat)).
% 1.38/0.48 thf(func_def_36, type, degree_real: (poly_real > nat)).
% 1.38/0.48 thf(func_def_37, type, poly_int2: (poly_int > int > int)).
% 1.38/0.48 thf(func_def_38, type, poly_nat2: (poly_nat > nat > nat)).
% 1.38/0.48 thf(func_def_39, type, poly_poly_real2: (poly_poly_real > poly_real > poly_real)).
% 1.38/0.48 thf(func_def_40, type, poly_real2: (poly_real > real > real)).
% 1.38/0.48 thf(func_def_41, type, coeff_int: (poly_int > nat > int)).
% 1.38/0.48 thf(func_def_42, type, coeff_nat: (poly_nat > nat > nat)).
% 1.38/0.48 thf(func_def_43, type, coeff_poly_real: (poly_poly_real > nat > poly_real)).
% 1.38/0.48 thf(func_def_44, type, coeff_real: (poly_real > nat > real)).
% 1.38/0.48 thf(func_def_45, type, power_power_int: (int > nat > int)).
% 1.38/0.48 thf(func_def_46, type, power_power_nat: (nat > nat > nat)).
% 1.38/0.48 thf(func_def_47, type, power_power_poly_int: (poly_int > nat > poly_int)).
% 1.38/0.48 thf(func_def_48, type, power_power_poly_nat: (poly_nat > nat > poly_nat)).
% 1.38/0.48 thf(func_def_49, type, power_2108872382y_real: (poly_real > nat > poly_real)).
% 1.38/0.48 thf(func_def_50, type, power_power_real: (real > nat > real)).
% 1.38/0.48 thf(func_def_51, type, field_1537545994s_real: set_real).
% 1.38/0.48 thf(func_def_52, type, divide_divide_int: (int > int > int)).
% 1.38/0.48 thf(func_def_53, type, divide_divide_nat: (nat > nat > nat)).
% 1.38/0.48 thf(func_def_54, type, divide1727078534y_real: (poly_real > poly_real > poly_real)).
% 1.38/0.48 thf(func_def_55, type, divide_divide_real: (real > real > real)).
% 1.38/0.48 thf(func_def_56, type, collect_real: ((real > $o) > set_real)).
% 1.38/0.48 thf(func_def_57, type, member_int: (int > set_int > $o)).
% 1.38/0.48 thf(func_def_58, type, member_poly_real: (poly_real > set_poly_real > $o)).
% 1.38/0.48 thf(func_def_59, type, member_real: (real > set_real > $o)).
% 1.38/0.48 thf(func_def_60, type, a: real).
% 1.38/0.48 thf(func_def_61, type, m: real).
% 1.38/0.48 thf(func_def_62, type, a2: int).
% 1.38/0.48 thf(func_def_63, type, b: int).
% 1.38/0.48 thf(func_def_64, type, n: nat).
% 1.38/0.48 thf(func_def_65, type, p: poly_real).
% 1.38/0.48 thf(func_def_66, type, roots: set_real).
% 1.38/0.48 thf(func_def_67, type, thesis: $o).
% 1.38/0.48 thf(func_def_68, type, x: real).
% 1.38/0.48 thf(func_def_72, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.38/0.48 thf(func_def_73, type, vAND: ($o > $o > $o)).
% 1.38/0.48 thf(func_def_74, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 1.38/0.48 thf(func_def_75, type, db1: !>[X0: $tType]:(X0)).
% 1.38/0.48 thf(func_def_76, type, db0: !>[X0: $tType]:(X0)).
% 1.38/0.48 thf(func_def_77, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 1.38/0.48 thf(func_def_78, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 1.38/0.48 thf(func_def_79, type, vNOT: ($o > $o)).
% 1.38/0.48 thf(func_def_80, type, db2: !>[X0: $tType]:(X0)).
% 1.38/0.48 thf(func_def_81, type, sK0: (int > int)).
% 1.38/0.48 thf(func_def_82, type, sK1: (nat > poly_real > nat)).
% 1.38/0.48 thf(func_def_83, type, sK2: (real > int)).
% 1.38/0.48 thf(func_def_84, type, sK3: (real > int)).
% 1.38/0.48 thf(func_def_85, type, sK4: (real > int)).
% 1.38/0.48 thf(func_def_86, type, sK5: (poly_poly_real > poly_real)).
% 1.38/0.48 thf(func_def_87, type, sK6: (poly_real > poly_real > nat)).
% 1.38/0.48 thf(func_def_88, type, sK7: (poly_real > nat)).
% 1.38/0.48 thf(func_def_89, type, sK8: (real > real > poly_real > real)).
% 1.38/0.48 thf(func_def_90, type, sK9: (real > real > poly_real > real)).
% 1.38/0.48 thf(func_def_91, type, sK10: (real > poly_real)).
% 1.38/0.48 thf(func_def_92, type, sK11: (nat > poly_nat > nat)).
% 1.38/0.48 thf(func_def_93, type, sK12: (poly_real > real)).
% 1.38/0.48 thf(func_def_94, type, sK13: (real > real)).
% 1.38/0.48 thf(func_def_95, type, sK14: poly_real).
% 1.38/0.48 thf(func_def_96, type, sK15: ((real > $o) > int)).
% 1.38/0.48 thf(func_def_97, type, sK16: (real > real)).
% 1.38/0.48 thf(func_def_98, type, sK17: (nat > real > int)).
% 1.38/0.48 thf(func_def_99, type, sK18: (nat > real > int)).
% 1.38/0.48 thf(func_def_100, type, sK19: (poly_int > nat > nat)).
% 1.38/0.48 thf(func_def_101, type, sK20: ((int > $o) > int)).
% 1.38/0.48 thf(func_def_102, type, sK21: (poly_real > nat)).
% 1.38/0.48 thf(func_def_103, type, sK22: (poly_real > real)).
% 1.38/0.48 thf(func_def_104, type, sK23: (poly_nat > nat > nat)).
% 1.38/0.48 thf(func_def_105, type, sK24: (poly_poly_real > nat > nat)).
% 1.38/0.48 thf(func_def_106, type, sK25: (poly_poly_real > nat > nat)).
% 1.38/0.48 thf(func_def_107, type, sK26: (poly_int > int)).
% 1.38/0.48 thf(func_def_108, type, sK27: (nat > poly_int > nat)).
% 1.38/0.48 thf(func_def_109, type, sK28: (poly_real > nat > nat)).
% 1.38/0.48 thf(func_def_111, type, inv_ring_1_of_int_real_30: (real > int)).
% 1.38/0.48 thf(func_def_112, type, inv_poly_real2_31: ((real > real) > poly_real)).
% 1.38/0.48 thf(func_def_113, type, sK32: (poly_real > poly_real > real)).
% 1.38/0.48 thf(f3,axiom,(
% 1.38/0.48 ! [X0 : nat] : (member_real @ (coeff_real @ p @ X0) @ ring_1_Ints_real)),
% 1.38/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_p_I1_J)).
% 1.38/0.48 thf(f4,axiom,(
% 1.38/0.48 (ord_less_int @ zero_zero_int @ b)),
% 1.38/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_b)).
% 1.38/0.48 thf(f6,axiom,(
% 1.38/0.48 (((poly_real2 @ p @ (divide_divide_real @ (ring_1_of_int_real @ a2) @ (ring_1_of_int_real @ b)))) != zero_zero_real)),
% 1.38/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_no__root)).
% 1.38/0.48 thf(f155,axiom,(
% 1.38/0.48 ! [X2 : int,X0 : poly_real,X1 : int] : (! [X3 : nat] : (member_real @ (coeff_real @ X0 @ X3) @ ring_1_Ints_real) => ((ord_less_int @ zero_zero_int @ X1) => ((((poly_real2 @ X0 @ (divide_divide_real @ (ring_1_of_int_real @ X2) @ (ring_1_of_int_real @ X1)))) != zero_zero_real) => (ord_less_eq_real @ (divide_divide_real @ one_one_real @ (power_power_real @ (ring_1_of_int_real @ X1) @ (degree_real @ X0))) @ (abs_abs_real @ (poly_real2 @ X0 @ (divide_divide_real @ (ring_1_of_int_real @ X2) @ (ring_1_of_int_real @ X1))))))))),
% 1.38/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_int__poly__rat__no__root__ge)).
% 1.38/0.48 thf(f354,conjecture,(
% 1.38/0.48 (ord_less_eq_real @ (divide_divide_real @ one_one_real @ (power_power_real @ (ring_1_of_int_real @ b) @ (degree_real @ p))) @ (abs_abs_real @ (poly_real2 @ p @ (divide_divide_real @ (ring_1_of_int_real @ a2) @ (ring_1_of_int_real @ b)))))),
% 1.38/0.48 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 1.38/0.48 thf(f355,negated_conjecture,(
% 1.38/0.48 ~(ord_less_eq_real @ (divide_divide_real @ one_one_real @ (power_power_real @ (ring_1_of_int_real @ b) @ (degree_real @ p))) @ (abs_abs_real @ (poly_real2 @ p @ (divide_divide_real @ (ring_1_of_int_real @ a2) @ (ring_1_of_int_real @ b)))))),
% 1.38/0.48 inference(negated_conjecture,[status(cth)],[f354])).
% 1.38/0.48 thf(f481,plain,(
% 1.38/0.48 ~(ord_less_eq_real @ (divide_divide_real @ one_one_real @ (power_power_real @ (ring_1_of_int_real @ b) @ (degree_real @ p))) @ (abs_abs_real @ (poly_real2 @ p @ (divide_divide_real @ (ring_1_of_int_real @ a2) @ (ring_1_of_int_real @ b)))))),
% 1.38/0.48 inference(rectify,[],[f355])).
% 1.38/0.48 thf(f482,plain,(
% 1.38/0.48 ~ (((ord_less_eq_real @ (divide_divide_real @ one_one_real @ (power_power_real @ (ring_1_of_int_real @ b) @ (degree_real @ p))) @ (abs_abs_real @ (poly_real2 @ p @ (divide_divide_real @ (ring_1_of_int_real @ a2) @ (ring_1_of_int_real @ b)))))) = $true)),
% 1.38/0.48 inference(fool_elimination,[],[f481])).
% 1.38/0.48 thf(f541,plain,(
% 1.38/0.48 (ord_less_int @ zero_zero_int @ b)),
% 1.38/0.48 inference(rectify,[],[f4])).
% 1.38/0.48 thf(f542,plain,(
% 1.38/0.48 (((ord_less_int @ zero_zero_int @ b)) = $true)),
% 1.38/0.48 inference(fool_elimination,[],[f541])).
% 1.38/0.48 thf(f581,plain,(
% 1.38/0.48 ! [X0 : int,X1 : poly_real,X2 : int] : (! [X3 : nat] : (member_real @ (coeff_real @ X1 @ X3) @ ring_1_Ints_real) => ((ord_less_int @ zero_zero_int @ X2) => ((zero_zero_real != ((poly_real2 @ X1 @ (divide_divide_real @ (ring_1_of_int_real @ X0) @ (ring_1_of_int_real @ X2))))) => (ord_less_eq_real @ (divide_divide_real @ one_one_real @ (power_power_real @ (ring_1_of_int_real @ X2) @ (degree_real @ X1))) @ (abs_abs_real @ (poly_real2 @ X1 @ (divide_divide_real @ (ring_1_of_int_real @ X0) @ (ring_1_of_int_real @ X2))))))))),
% 1.38/0.48 inference(rectify,[],[f155])).
% 1.38/0.48 thf(f582,plain,(
% 1.38/0.48 ! [X0 : int,X2 : int,X1 : poly_real] : (! [X3 : nat] : (((member_real @ (coeff_real @ X1 @ X3) @ ring_1_Ints_real)) = $true) => ((((ord_less_int @ zero_zero_int @ X2)) = $true) => ((zero_zero_real != ((poly_real2 @ X1 @ (divide_divide_real @ (ring_1_of_int_real @ X0) @ (ring_1_of_int_real @ X2))))) => (((ord_less_eq_real @ (divide_divide_real @ one_one_real @ (power_power_real @ (ring_1_of_int_real @ X2) @ (degree_real @ X1))) @ (abs_abs_real @ (poly_real2 @ X1 @ (divide_divide_real @ (ring_1_of_int_real @ X0) @ (ring_1_of_int_real @ X2)))))) = $true))))),
% 1.38/0.48 inference(fool_elimination,[],[f581])).
% 1.38/0.48 thf(f652,plain,(
% 1.38/0.48 ! [X0 : nat] : (member_real @ (coeff_real @ p @ X0) @ ring_1_Ints_real)),
% 1.38/0.48 inference(rectify,[],[f3])).
% 1.38/0.48 thf(f653,plain,(
% 1.38/0.48 ! [X0 : nat] : (((member_real @ (coeff_real @ p @ X0) @ ring_1_Ints_real)) = $true)),
% 1.38/0.48 inference(fool_elimination,[],[f652])).
% 1.38/0.48 thf(f812,plain,(
% 1.38/0.48 (((ord_less_eq_real @ (divide_divide_real @ one_one_real @ (power_power_real @ (ring_1_of_int_real @ b) @ (degree_real @ p))) @ (abs_abs_real @ (poly_real2 @ p @ (divide_divide_real @ (ring_1_of_int_real @ a2) @ (ring_1_of_int_real @ b)))))) != $true)),
% 1.38/0.48 inference(flattening,[],[f482])).
% 1.38/0.48 thf(f982,plain,(
% 1.38/0.48 ! [X0 : int,X2 : int,X1 : poly_real] : ((((((ord_less_eq_real @ (divide_divide_real @ one_one_real @ (power_power_real @ (ring_1_of_int_real @ X2) @ (degree_real @ X1))) @ (abs_abs_real @ (poly_real2 @ X1 @ (divide_divide_real @ (ring_1_of_int_real @ X0) @ (ring_1_of_int_real @ X2)))))) = $true) | (zero_zero_real = ((poly_real2 @ X1 @ (divide_divide_real @ (ring_1_of_int_real @ X0) @ (ring_1_of_int_real @ X2)))))) | (((ord_less_int @ zero_zero_int @ X2)) != $true)) | ? [X3 : nat] : (((member_real @ (coeff_real @ X1 @ X3) @ ring_1_Ints_real)) != $true))),
% 1.38/0.48 inference(ennf_transformation,[],[f582])).
% 1.38/0.48 thf(f983,plain,(
% 1.38/0.48 ! [X0 : int,X1 : poly_real,X2 : int] : ((((ord_less_int @ zero_zero_int @ X2)) != $true) | ? [X3 : nat] : (((member_real @ (coeff_real @ X1 @ X3) @ ring_1_Ints_real)) != $true) | (((ord_less_eq_real @ (divide_divide_real @ one_one_real @ (power_power_real @ (ring_1_of_int_real @ X2) @ (degree_real @ X1))) @ (abs_abs_real @ (poly_real2 @ X1 @ (divide_divide_real @ (ring_1_of_int_real @ X0) @ (ring_1_of_int_real @ X2)))))) = $true) | (zero_zero_real = ((poly_real2 @ X1 @ (divide_divide_real @ (ring_1_of_int_real @ X0) @ (ring_1_of_int_real @ X2))))))),
% 1.38/0.48 inference(flattening,[],[f982])).
% 1.38/0.48 thf(f1122,plain,(
% 1.38/0.48 ! [X0 : int,X1 : poly_real,X2 : int] : ((((ord_less_int @ zero_zero_int @ X2)) != $true) | (((member_real @ (coeff_real @ X1 @ (sK7 @ X1)) @ ring_1_Ints_real)) != $true) | (((ord_less_eq_real @ (divide_divide_real @ one_one_real @ (power_power_real @ (ring_1_of_int_real @ X2) @ (degree_real @ X1))) @ (abs_abs_real @ (poly_real2 @ X1 @ (divide_divide_real @ (ring_1_of_int_real @ X0) @ (ring_1_of_int_real @ X2)))))) = $true) | (zero_zero_real = ((poly_real2 @ X1 @ (divide_divide_real @ (ring_1_of_int_real @ X0) @ (ring_1_of_int_real @ X2))))))),
% 1.38/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,sK0 @ X0)],[f983])).
% 1.38/0.48 thf(f1353,plain,(
% 1.38/0.48 (((ord_less_eq_real @ (divide_divide_real @ one_one_real @ (power_power_real @ (ring_1_of_int_real @ b) @ (degree_real @ p))) @ (abs_abs_real @ (poly_real2 @ p @ (divide_divide_real @ (ring_1_of_int_real @ a2) @ (ring_1_of_int_real @ b)))))) != $true)),
% 1.38/0.48 inference(cnf_transformation,[],[f812])).
% 1.38/0.48 thf(f1386,plain,(
% 1.38/0.48 ( ! [X2 : int,X0 : int,X1 : poly_real] : ((((ord_less_eq_real @ (divide_divide_real @ one_one_real @ (power_power_real @ (ring_1_of_int_real @ X2) @ (degree_real @ X1))) @ (abs_abs_real @ (poly_real2 @ X1 @ (divide_divide_real @ (ring_1_of_int_real @ X0) @ (ring_1_of_int_real @ X2)))))) = $true) | (zero_zero_real = ((poly_real2 @ X1 @ (divide_divide_real @ (ring_1_of_int_real @ X0) @ (ring_1_of_int_real @ X2))))) | (((ord_less_int @ zero_zero_int @ X2)) != $true) | (((member_real @ (coeff_real @ X1 @ (sK7 @ X1)) @ ring_1_Ints_real)) != $true)) )),
% 1.38/0.48 inference(cnf_transformation,[],[f1122])).
% 1.38/0.48 thf(f1523,plain,(
% 1.38/0.48 (zero_zero_real != ((poly_real2 @ p @ (divide_divide_real @ (ring_1_of_int_real @ a2) @ (ring_1_of_int_real @ b)))))),
% 1.38/0.48 inference(cnf_transformation,[],[f6])).
% 1.38/0.48 thf(f1706,plain,(
% 1.38/0.48 (((ord_less_int @ zero_zero_int @ b)) = $true)),
% 1.38/0.48 inference(cnf_transformation,[],[f542])).
% 1.38/0.48 thf(f1810,plain,(
% 1.38/0.48 ( ! [X0 : nat] : ((((member_real @ (coeff_real @ p @ X0) @ ring_1_Ints_real)) = $true)) )),
% 1.38/0.48 inference(cnf_transformation,[],[f653])).
% 1.38/0.48 thf(f2099,definition,(
% 1.38/0.48 spl29_18 <=> (((ord_less_eq_real @ (divide_divide_real @ one_one_real @ (power_power_real @ (ring_1_of_int_real @ b) @ (degree_real @ p))) @ (abs_abs_real @ (poly_real2 @ p @ (divide_divide_real @ (ring_1_of_int_real @ a2) @ (ring_1_of_int_real @ b)))))) = $true)),
% 1.38/0.48 introduced(definition,[new_symbols(definition,[spl29_18])],[avatar_definition])).
% 1.38/0.48 thf(f2101,plain,(
% 1.38/0.48 (((ord_less_eq_real @ (divide_divide_real @ one_one_real @ (power_power_real @ (ring_1_of_int_real @ b) @ (degree_real @ p))) @ (abs_abs_real @ (poly_real2 @ p @ (divide_divide_real @ (ring_1_of_int_real @ a2) @ (ring_1_of_int_real @ b)))))) != $true) | spl29_18),
% 1.38/0.48 inference(avatar_component_clause,[],[f2099])).
% 1.38/0.48 thf(f2102,plain,(
% 1.38/0.48 ~spl29_18),
% 1.38/0.48 inference(avatar_split_clause,[],[f1353,f2099])).
% 1.38/0.48 thf(f2159,definition,(
% 1.38/0.48 spl29_30 <=> (zero_zero_real = ((poly_real2 @ p @ (divide_divide_real @ (ring_1_of_int_real @ a2) @ (ring_1_of_int_real @ b)))))),
% 1.38/0.48 introduced(definition,[new_symbols(definition,[spl29_30])],[avatar_definition])).
% 1.38/0.48 thf(f2161,plain,(
% 1.38/0.48 (zero_zero_real != ((poly_real2 @ p @ (divide_divide_real @ (ring_1_of_int_real @ a2) @ (ring_1_of_int_real @ b))))) | spl29_30),
% 1.38/0.48 inference(avatar_component_clause,[],[f2159])).
% 1.38/0.48 thf(f2162,plain,(
% 1.38/0.48 ~spl29_30),
% 1.38/0.48 inference(avatar_split_clause,[],[f1523,f2159])).
% 1.38/0.48 thf(f2248,definition,(
% 1.38/0.48 spl29_48 <=> (((ord_less_int @ zero_zero_int @ b)) = $true)),
% 1.38/0.48 introduced(definition,[new_symbols(definition,[spl29_48])],[avatar_definition])).
% 1.38/0.48 thf(f2250,plain,(
% 1.38/0.48 (((ord_less_int @ zero_zero_int @ b)) = $true) | ~spl29_48),
% 1.38/0.48 inference(avatar_component_clause,[],[f2248])).
% 1.38/0.48 thf(f2251,plain,(
% 1.38/0.48 spl29_48),
% 1.38/0.48 inference(avatar_split_clause,[],[f1706,f2248])).
% 1.38/0.48 thf(f3981,plain,(
% 1.38/0.48 ($true != $true) | (((member_real @ (coeff_real @ p @ (sK7 @ p)) @ ring_1_Ints_real)) != $true) | (((ord_less_int @ zero_zero_int @ b)) != $true) | (zero_zero_real = ((poly_real2 @ p @ (divide_divide_real @ (ring_1_of_int_real @ a2) @ (ring_1_of_int_real @ b))))) | spl29_18),
% 1.38/0.48 inference(superposition,[],[f2101,f1386])).
% 1.38/0.48 thf(f3982,plain,(
% 1.38/0.48 (zero_zero_real = ((poly_real2 @ p @ (divide_divide_real @ (ring_1_of_int_real @ a2) @ (ring_1_of_int_real @ b))))) | (((ord_less_int @ zero_zero_int @ b)) != $true) | (((member_real @ (coeff_real @ p @ (sK7 @ p)) @ ring_1_Ints_real)) != $true) | spl29_18),
% 1.38/0.48 inference(trivial_inequality_removal,[],[f3981])).
% 1.38/0.48 thf(f3987,plain,(
% 1.38/0.48 (((ord_less_int @ zero_zero_int @ b)) != $true) | (((member_real @ (coeff_real @ p @ (sK7 @ p)) @ ring_1_Ints_real)) != $true) | (spl29_18 | spl29_30)),
% 1.38/0.48 inference(forward_subsumption_resolution,[],[f3982,f2161])).
% 1.38/0.48 thf(f3999,plain,(
% 1.38/0.48 (((member_real @ (coeff_real @ p @ (sK7 @ p)) @ ring_1_Ints_real)) != $true) | (spl29_18 | spl29_30 | ~spl29_48)),
% 1.38/0.48 inference(forward_subsumption_resolution,[],[f3987,f2250])).
% 1.38/0.48 thf(f4009,plain,(
% 1.38/0.48 $false | (spl29_18 | spl29_30 | ~spl29_48)),
% 1.38/0.48 inference(forward_subsumption_resolution,[],[f3999,f1810])).
% 1.38/0.48 thf(f4010,plain,(
% 1.38/0.48 spl29_18 | spl29_30 | ~spl29_48),
% 1.38/0.48 inference(avatar_contradiction_clause,[],[f4009])).
% 1.38/0.48 cnf(s18, plain, ~spl29_18, inference(sat_conversion,[],[f2102])).
% 1.38/0.48 cnf(s31, plain, ~spl29_30, inference(sat_conversion,[],[f2162])).
% 1.38/0.48 cnf(s52, plain, spl29_48, inference(sat_conversion,[],[f2251])).
% 1.38/0.48 cnf(s230, plain, spl29_18 | spl29_30 | ~spl29_48, inference(sat_conversion,[],[f4010])).
% 1.38/0.48 cnf(s262, plain, spl29_18, inference(rat,[],[s230,s52,s31])).
% 1.38/0.48 cnf(s268, plain, $false, inference(rat,[],[s18,s262])).
% 1.38/0.48 thf(f4012,plain,(
% 1.38/0.48 $false),
% 1.38/0.48 inference(avatar_sat_refutation,[],[s268])).
% 1.38/0.48 % SZS output end Proof for theBenchmark
% 1.38/0.48 % (272504)------------------------------
% 1.38/0.48 % (272504)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.38/0.48 % (272504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.38/0.48 % (272504)CaDiCaL version: 2.1.3
% 1.38/0.48 % (272504)Termination reason: Refutation
% 1.38/0.48 % (272504)Time elapsed: 0.169 s
% 1.38/0.48 % (272504)Peak memory usage: 16 MB
% 1.38/0.48 % (272504)Instructions burned: 315 (million)
% 1.38/0.48 % (272496)Success in time 0.224 s
% 1.38/0.48 % Vampire exiting
%------------------------------------------------------------------------------