%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COM192^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 07:46:25 AM UTC 2026
% Result : Theorem 0.61s 0.41s
% Output : Refutation 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM192^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n008.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 17:51:24 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.26 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.61/0.41 % (3498976)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.61/0.41 % (3498985)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4131229201:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.61/0.41 % (3498987)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.61/0.41 % (3498987)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
% 0.61/0.41 % (3498981)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=956912432:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.61/0.41 % (3498982)lrs+10_16_si=on:nwc=1.5:random_seed=1489807067:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.61/0.41 % (3498983)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1543462957:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.61/0.41 % (3498984)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=3971138273: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)
% 0.61/0.41 % (3498986)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=711457442:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.61/0.41 % (3498987)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=1107012855:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.61/0.41 % (3498985)Instruction limit reached!
% 0.61/0.41 % (3498985)------------------------------
% 0.61/0.41 % (3498985)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (3498985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (3498985)CaDiCaL version: 2.1.3
% 0.61/0.41 % (3498985)Termination reason: Instruction limit
% 0.61/0.41 % (3498985)Termination phase: Property scanning
% 0.61/0.41 % (3498985)Time elapsed: 0.007 s
% 0.61/0.41 % (3498985)Peak memory usage: 10 MB
% 0.61/0.41 % (3498985)Instructions burned: 28 (million)
% 0.61/0.41 % (3498983)Instruction limit reached!
% 0.61/0.41 % (3498983)------------------------------
% 0.61/0.41 % (3498983)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (3498983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (3498983)CaDiCaL version: 2.1.3
% 0.61/0.41 % (3498983)Termination reason: Instruction limit
% 0.61/0.41 % (3498983)Termination phase: shuffling
% 0.61/0.41 % (3498983)Time elapsed: 0.002 s
% 0.61/0.41 % (3498983)Peak memory usage: 10 MB
% 0.61/0.41 % (3498983)Instructions burned: 4 (million)
% 0.61/0.41 % (3498982)Instruction limit reached!
% 0.61/0.41 % (3498982)------------------------------
% 0.61/0.41 % (3498982)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (3498982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (3498982)CaDiCaL version: 2.1.3
% 0.61/0.41 % (3498982)Termination reason: Instruction limit
% 0.61/0.41 % (3498982)Termination phase: Property scanning
% 0.61/0.41 % (3498982)Time elapsed: 0.010 s
% 0.61/0.41 % (3498982)Peak memory usage: 10 MB
% 0.61/0.41 % (3498982)Instructions burned: 20 (million)
% 0.61/0.41 % (3498995)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4009272224:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.41 % (3498995)Instruction limit reached!
% 0.61/0.41 % (3498995)------------------------------
% 0.61/0.41 % (3498995)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (3498995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (3498995)CaDiCaL version: 2.1.3
% 0.61/0.41 % (3498995)Termination reason: Instruction limit
% 0.61/0.41 % (3498995)Termination phase: shuffling
% 0.61/0.41 % (3498995)Time elapsed: 0.002 s
% 0.61/0.41 % (3498995)Peak memory usage: 10 MB
% 0.61/0.41 % (3498995)Instructions burned: 7 (million)
% 0.61/0.41 % (3498996)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=407902598:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.61/0.41 % (3498999)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2257047830:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.61/0.41 % (3498996)Instruction limit reached!
% 0.61/0.41 % (3498996)------------------------------
% 0.61/0.41 % (3498996)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (3498996)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (3498996)CaDiCaL version: 2.1.3
% 0.61/0.41 % (3498996)Termination reason: Instruction limit
% 0.61/0.41 % (3498996)Termination phase: shuffling
% 0.61/0.41 % (3498996)Time elapsed: 0.004 s
% 0.61/0.41 % (3498996)Peak memory usage: 10 MB
% 0.61/0.41 % (3498996)Instructions burned: 6 (million)
% 0.61/0.41 % (3498997)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.41 % (3498999)Instruction limit reached!
% 0.61/0.41 % (3498999)------------------------------
% 0.61/0.41 % (3498999)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (3498999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (3498999)CaDiCaL version: 2.1.3
% 0.61/0.41 % (3498999)Termination reason: Instruction limit
% 0.61/0.41 % (3498999)Termination phase: shuffling
% 0.61/0.41 % (3498999)Time elapsed: 0.003 s
% 0.61/0.41 % (3498999)Peak memory usage: 10 MB
% 0.61/0.41 % (3498999)Instructions burned: 12 (million)
% 0.61/0.41 % (3498997)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3761896918:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.61/0.41 % (3498997)Instruction limit reached!
% 0.61/0.41 % (3498997)------------------------------
% 0.61/0.41 % (3498997)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (3498997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (3498997)CaDiCaL version: 2.1.3
% 0.61/0.41 % (3498997)Termination reason: Instruction limit
% 0.61/0.41 % (3498997)Termination phase: shuffling
% 0.61/0.41 % (3498997)Time elapsed: 0.004 s
% 0.61/0.41 % (3498997)Peak memory usage: 10 MB
% 0.61/0.41 % (3498997)Instructions burned: 8 (million)
% 0.61/0.41 % (3498986)Instruction limit reached!
% 0.61/0.41 % (3498986)------------------------------
% 0.61/0.41 % (3498986)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (3498986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (3498986)CaDiCaL version: 2.1.3
% 0.61/0.41 % (3498986)Termination reason: Instruction limit
% 0.61/0.41 % (3498986)Termination phase: Property scanning
% 0.61/0.41 % (3498986)Time elapsed: 0.037 s
% 0.61/0.41 % (3498986)Peak memory usage: 12 MB
% 0.61/0.41 % (3498986)Instructions burned: 75 (million)
% 0.61/0.41 % (3499003)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=2190111444:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.61/0.41 % (3499002)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
% 0.61/0.41 % (3499002)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.61/0.41 % (3499002)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1471761014:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.61/0.41 % (3499006)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.61/0.41 % (3499005)lrs+10_1_si=on:cs=on:random_seed=1762106546:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.61/0.41 % (3499002)Instruction limit reached!
% 0.61/0.41 % (3499002)------------------------------
% 0.61/0.41 % (3499002)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (3499002)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (3499002)CaDiCaL version: 2.1.3
% 0.61/0.41 % (3499002)Termination reason: Instruction limit
% 0.61/0.41 % (3499002)Termination phase: shuffling
% 0.61/0.41 % (3499002)Time elapsed: 0.014 s
% 0.61/0.41 % (3499002)Peak memory usage: 10 MB
% 0.61/0.41 % (3499002)Instructions burned: 29 (million)
% 0.61/0.41 % (3499005)Instruction limit reached!
% 0.61/0.41 % (3499005)------------------------------
% 0.61/0.41 % (3499005)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (3499005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (3499005)CaDiCaL version: 2.1.3
% 0.61/0.41 % (3499005)Termination reason: Instruction limit
% 0.61/0.41 % (3499005)Termination phase: shuffling
% 0.61/0.41 % (3499005)Time elapsed: 0.004 s
% 0.61/0.41 % (3499005)Peak memory usage: 10 MB
% 0.61/0.41 % (3499005)Instructions burned: 12 (million)
% 0.61/0.41 % (3499006)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=567409087:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.61/0.41 % (3499006)Instruction limit reached!
% 0.61/0.41 % (3499006)------------------------------
% 0.61/0.41 % (3499006)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (3499006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (3499006)CaDiCaL version: 2.1.3
% 0.61/0.41 % (3499006)Termination reason: Instruction limit
% 0.61/0.41 % (3499006)Termination phase: shuffling
% 0.61/0.41 % (3499006)Time elapsed: 0.002 s
% 0.61/0.41 % (3499006)Peak memory usage: 10 MB
% 0.61/0.41 % (3499006)Instructions burned: 3 (million)
% 0.61/0.41 % (3498981)Instruction limit reached!
% 0.61/0.41 % (3498981)------------------------------
% 0.61/0.41 % (3498981)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (3498981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (3498981)CaDiCaL version: 2.1.3
% 0.61/0.41 % (3498981)Termination reason: Instruction limit
% 0.61/0.41 % (3498981)Termination phase: Property scanning
% 0.61/0.41 % (3498981)Time elapsed: 0.068 s
% 0.61/0.41 % (3498981)Peak memory usage: 12 MB
% 0.61/0.41 % (3498981)Instructions burned: 87 (million)
% 0.61/0.41 % (3499003)Instruction limit reached!
% 0.61/0.41 % (3499003)------------------------------
% 0.61/0.41 % (3499003)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (3499003)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (3499003)CaDiCaL version: 2.1.3
% 0.61/0.41 % (3499003)Termination reason: Instruction limit
% 0.61/0.41 % (3499003)Termination phase: Preprocessing 3
% 0.61/0.41 % (3499003)Time elapsed: 0.029 s
% 0.61/0.41 % (3499003)Peak memory usage: 11 MB
% 0.61/0.41 % (3499003)Instructions burned: 88 (million)
% 0.61/0.41 % (3499011)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2196573729:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.61/0.41 % (3499010)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2807692496:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.61/0.41 % (3498987)Instruction limit reached!
% 0.61/0.41 % (3498987)------------------------------
% 0.61/0.41 % (3498987)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.41 % (3498987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.41 % (3498987)CaDiCaL version: 2.1.3
% 0.61/0.41 % (3498987)Termination reason: Instruction limit
% 0.61/0.41 % (3498987)Termination phase: Saturation
% 0.61/0.41 % (3498987)Time elapsed: 0.078 s
% 0.61/0.41 % (3498987)Peak memory usage: 14 MB
% 0.61/0.41 % (3498987)Instructions burned: 157 (million)
% 0.61/0.41 % (3499013)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2456153082:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.61/0.41 % (3499014)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1896562463:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.61/0.41 % (3499016)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=475514305:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.61/0.41 % (3499011) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3498976-3499011"...
% 0.61/0.41 % (3499011)...printing done.
% 0.61/0.41 % (3499011)Refutation found. Thanks to Tanya!
% 0.61/0.41 % SZS status Theorem for theBenchmark
% 0.61/0.41 % SZS output start Proof for theBenchmark
% 0.61/0.41 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 0.61/0.41 thf(type_def_6, type, sum_sum: ($tType * $tType) > $tType).
% 0.61/0.41 thf(type_def_7, type, option: $tType > $tType).
% 0.61/0.41 thf(type_def_8, type, dtree: $tType).
% 0.61/0.41 thf(type_def_9, type, set: $tType > $tType).
% 0.61/0.41 thf(type_def_10, type, t: $tType).
% 0.61/0.41 thf(type_def_11, type, n: $tType).
% 0.61/0.41 thf(type_def_12, type, itself: $tType > $tType).
% 0.61/0.41 thf(type_def_13, type, sTfun: ($tType * $tType) > $tType).
% 0.61/0.41 thf(func_def_0, type, type: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.41 thf(func_def_1, type, top: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.41 thf(func_def_2, type, finite_finite: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.41 thf(func_def_3, type, semiring_char_0: !>[X0: $tType]:((itself @ X0 > $o))).
% 0.61/0.41 thf(func_def_4, type, node: (n > set @ sum_sum @ t @ dtree > dtree)).
% 0.61/0.41 thf(func_def_5, type, cont: (dtree > set @ sum_sum @ t @ dtree)).
% 0.61/0.41 thf(func_def_6, type, corec: !>[X0: $tType]:(((X0 > n) > (X0 > set @ sum_sum @ t @ sum_sum @ dtree @ X0) > X0 > dtree))).
% 0.61/0.41 thf(func_def_7, type, root: (dtree > n)).
% 0.61/0.41 thf(func_def_8, type, unfold: !>[X0: $tType]:(((X0 > n) > (X0 > set @ sum_sum @ t @ X0) > X0 > dtree))).
% 0.61/0.41 thf(func_def_9, type, finite_finite2: !>[X0: $tType]:((set @ X0 > $o))).
% 0.61/0.41 thf(func_def_10, type, comp: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X2 > X0) > X2 > X1))).
% 0.61/0.41 thf(func_def_11, type, id: !>[X0: $tType]:((X0 > X0))).
% 0.61/0.41 thf(func_def_12, type, inj_on: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > $o))).
% 0.61/0.41 thf(func_def_13, type, gram_L1451583624elle_H: (dtree > n > dtree)).
% 0.61/0.41 thf(func_def_14, type, gram_L1221482011le_H_c: (dtree > n > set @ sum_sum @ t @ n)).
% 0.61/0.41 thf(func_def_15, type, gram_L1221482026le_H_r: (dtree > n > n)).
% 0.61/0.41 thf(func_def_16, type, gram_L1451583635elle_S: (n > set @ sum_sum @ t @ n)).
% 0.61/0.41 thf(func_def_17, type, gram_L1231612515_deftr: (n > dtree)).
% 0.61/0.41 thf(func_def_18, type, gram_L1004374585hsubst: (dtree > dtree > dtree)).
% 0.61/0.41 thf(func_def_19, type, gram_L1905609002ubst_c: (dtree > dtree > set @ sum_sum @ t @ dtree)).
% 0.61/0.41 thf(func_def_20, type, gram_L1905609017ubst_r: (dtree > n)).
% 0.61/0.41 thf(func_def_21, type, gram_L805317441_inFr2: (set @ n > dtree > t > $o)).
% 0.61/0.41 thf(func_def_22, type, gram_L830233218_inItr: (set @ n > dtree > n > $o)).
% 0.61/0.41 thf(func_def_23, type, gram_L315592705e_pick: (dtree > n > dtree)).
% 0.61/0.41 thf(func_def_24, type, gram_L716654942_subtr: (set @ n > dtree > dtree > $o)).
% 0.61/0.41 thf(func_def_25, type, gram_L1614515765ubtrOf: (dtree > n > dtree)).
% 0.61/0.41 thf(func_def_26, type, gram_L864798063lle_wf: (dtree > $o)).
% 0.61/0.41 thf(func_def_27, type, if: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.61/0.41 thf(func_def_28, type, top_top: !>[X0: $tType]:(X0)).
% 0.61/0.41 thf(func_def_29, type, type2: !>[X0: $tType]:(itself @ X0)).
% 0.61/0.41 thf(func_def_30, type, collect: !>[X0: $tType]:(((X0 > $o) > set @ X0))).
% 0.61/0.41 thf(func_def_31, type, image: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X0 > set @ X1))).
% 0.61/0.41 thf(func_def_32, type, vimage: !>[X0: $tType, X1: $tType]:(((X0 > X1) > set @ X1 > set @ X0))).
% 0.61/0.41 thf(func_def_33, type, sum_Inl: !>[X0: $tType, X1: $tType]:((X0 > sum_sum @ X0 @ X1))).
% 0.61/0.41 thf(func_def_34, type, sum_Inr: !>[X0: $tType, X1: $tType]:((X0 > sum_sum @ X1 @ X0))).
% 0.61/0.41 thf(func_def_35, type, sum_map_sum: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(((X0 > X1) > (X2 > X3) > sum_sum @ X0 @ X2 > sum_sum @ X1 @ X3))).
% 0.61/0.41 thf(func_def_36, type, sum_rec_sum: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X2 > X1) > sum_sum @ X0 @ X2 > X1))).
% 0.61/0.41 thf(func_def_37, type, sum_case_sum: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X1) > (X2 > X1) > sum_sum @ X0 @ X2 > X1))).
% 0.61/0.41 thf(func_def_38, type, member: !>[X0: $tType]:((X0 > set @ X0 > $o))).
% 0.61/0.41 thf(func_def_39, type, a: t).
% 0.61/0.41 thf(func_def_40, type, n2: n).
% 0.61/0.41 thf(func_def_41, type, t_tr: sum_sum @ t @ dtree).
% 0.61/0.41 thf(func_def_42, type, tr0: dtree).
% 0.61/0.41 thf(func_def_46, type, db1: !>[X0: $tType]:(X0)).
% 0.61/0.41 thf(func_def_47, type, db0: !>[X0: $tType]:(X0)).
% 0.61/0.41 thf(func_def_48, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.61/0.41 thf(func_def_49, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.61/0.41 thf(func_def_50, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.61/0.41 thf(func_def_51, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.61/0.41 thf(func_def_52, type, vAND: ($o > $o > $o)).
% 0.61/0.41 thf(func_def_53, type, vOR: ($o > $o > $o)).
% 0.61/0.41 thf(func_def_54, type, db3: !>[X0: $tType]:(X0)).
% 0.61/0.41 thf(func_def_55, type, db2: !>[X0: $tType]:(X0)).
% 0.61/0.41 thf(func_def_56, type, db4: !>[X0: $tType]:(X0)).
% 0.61/0.41 thf(func_def_57, type, db6: !>[X0: $tType]:(X0)).
% 0.61/0.41 thf(func_def_58, type, db5: !>[X0: $tType]:(X0)).
% 0.61/0.41 thf(func_def_59, type, vIMP: ($o > $o > $o)).
% 0.61/0.41 thf(func_def_60, type, sK0: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X0))).
% 0.61/0.41 thf(func_def_61, type, sK1: !>[X0: $tType, X1: $tType]:((sum_sum @ X0 @ X1 > X1))).
% 0.61/0.41 thf(func_def_62, type, sK2: !>[X0: $tType, X1: $tType, X2: $tType]:((set @ X2 > (X1 > X0) > (X2 > X1) > (X1 > X0) > X2))).
% 0.61/0.41 thf(func_def_63, type, sK3: (dtree > dtree > n)).
% 0.61/0.41 thf(func_def_64, type, sK4: !>[X0: $tType, X1: $tType]:(((X1 > X0) > (X1 > X0) > X1))).
% 0.61/0.41 thf(func_def_65, type, sK5: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > X1))).
% 0.61/0.41 thf(func_def_66, type, sK6: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > X0))).
% 0.61/0.41 thf(func_def_67, type, sK7: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1) > (X2 > X1) > (X1 > X0) > (X1 > X0) > X1))).
% 0.61/0.41 thf(func_def_68, type, sK8: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1) > (X2 > X1) > (X1 > X0) > (X1 > X0) > X1))).
% 0.61/0.41 thf(func_def_69, type, sK9: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2) > X2 > sum_sum @ X1 @ X0 > X0))).
% 0.61/0.41 thf(func_def_70, type, sK10: !>[X0: $tType, X1: $tType, X2: $tType]:((sum_sum @ X0 @ X1 > (X0 > X2) > X2 > X0))).
% 0.61/0.41 thf(func_def_71, type, sK11: !>[X0: $tType, X1: $tType, X2: $tType]:(((X0 > X2) > set @ sum_sum @ X1 @ X0 > X2 > X0))).
% 0.61/0.41 thf(func_def_72, type, sK12: !>[X0: $tType, X1: $tType, X2: $tType]:(((X1 > X0) > (X2 > X1) > (X1 > X0) > X1))).
% 0.61/0.41 thf(func_def_73, type, sK13: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > $o > (sum_sum @ X2 @ X0 > X1) > X2))).
% 0.61/0.41 thf(func_def_74, type, sK14: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > $o > (sum_sum @ X2 @ X0 > X1) > X0))).
% 0.61/0.41 thf(func_def_75, type, sK15: (dtree > n)).
% 0.61/0.41 thf(func_def_76, type, sK16: !>[X0: $tType, X1: $tType]:(((sum_sum @ X0 @ X1 > $o) > X1))).
% 0.61/0.41 thf(func_def_77, type, sK17: !>[X0: $tType, X1: $tType]:(((sum_sum @ X0 @ X1 > $o) > X0))).
% 0.61/0.41 thf(func_def_78, type, sK18: !>[X0: $tType, X1: $tType, X2: $tType]:(((X2 > X1) > (X2 > X1) > (X0 > X2) > X2))).
% 0.61/0.41 thf(func_def_79, type, sK19: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > X1))).
% 0.61/0.41 thf(func_def_80, type, sK20: !>[X0: $tType, X1: $tType]:((sum_sum @ X1 @ X0 > X0))).
% 0.61/0.41 thf(func_def_81, type, vNOT: ($o > $o)).
% 0.61/0.41 thf(f40,axiom,(
% 0.61/0.41 ! [X0 : $tType] : ((^[X1 : X0] : (X1)) = id @ X0)),
% 0.61/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_id__def)).
% 0.61/0.41 thf(f58,axiom,(
% 0.61/0.41 ! [X1 : $tType,X2 : $tType,X3 : $tType,X0 : $tType,X5 : (X0 > X1),X6 : X3,X4 : (X3 > X2)] : (((sum_map_sum @ X3 @ X2 @ X0 @ X1 @ X4 @ X5 @ (sum_Inl @ X3 @ X0 @ X6))) = ((sum_Inl @ X2 @ X1 @ (X4 @ X6))))),
% 0.61/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_map__sum_Osimps_I1_J)).
% 0.61/0.41 thf(f271,axiom,(
% 0.61/0.41 (t_tr = ((sum_Inl @ t @ dtree @ a)))),
% 0.61/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2)).
% 0.61/0.41 thf(f272,conjecture,(
% 0.61/0.41 (((sum_map_sum @ t @ t @ dtree @ n @ id @ t @ (comp @ n @ n @ dtree @ (comp @ dtree @ n @ n @ root @ (gram_L1451583624elle_H @ tr0)) @ root) @ t_tr)) = ((sum_map_sum @ t @ t @ dtree @ n @ id @ t @ root @ t_tr)))),
% 0.61/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3)).
% 0.61/0.41 thf(f273,negated_conjecture,(
% 0.61/0.41 ~ (((sum_map_sum @ t @ t @ dtree @ n @ id @ t @ (comp @ n @ n @ dtree @ (comp @ dtree @ n @ n @ root @ (gram_L1451583624elle_H @ tr0)) @ root) @ t_tr)) = ((sum_map_sum @ t @ t @ dtree @ n @ id @ t @ root @ t_tr)))),
% 0.61/0.41 inference(negated_conjecture,[status(cth)],[f272])).
% 0.61/0.41 thf(f519,plain,(
% 0.61/0.41 ! [X0 : $tType] : (id @ X0 = (^[Y0 : X0]: (Y0)))),
% 0.61/0.41 inference(fool_elimination,[],[f40])).
% 0.61/0.41 thf(f569,plain,(
% 0.61/0.41 (((sum_map_sum @ t @ t @ dtree @ n @ id @ t @ (comp @ n @ n @ dtree @ (comp @ dtree @ n @ n @ root @ (gram_L1451583624elle_H @ tr0)) @ root) @ t_tr)) != ((sum_map_sum @ t @ t @ dtree @ n @ id @ t @ root @ t_tr)))),
% 0.61/0.41 inference(flattening,[],[f273])).
% 0.61/0.41 thf(f573,plain,(
% 0.61/0.41 ! [X2 : $tType,X3 : $tType,X0 : $tType,X1 : $tType,X4 : (X3 > X0),X6 : (X2 > X1),X5 : X2] : (((sum_map_sum @ X2 @ X1 @ X3 @ X0 @ X6 @ X4 @ (sum_Inl @ X2 @ X3 @ X5))) = ((sum_Inl @ X1 @ X0 @ (X6 @ X5))))),
% 0.61/0.41 inference(rectify,[],[f58])).
% 0.61/0.41 thf(f733,plain,(
% 0.61/0.41 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : (X1 > X2),X5 : (X0 > X3),X6 : X0] : (((sum_Inl @ X3 @ X2 @ (X5 @ X6))) = ((sum_map_sum @ X0 @ X3 @ X1 @ X2 @ X5 @ X4 @ (sum_Inl @ X0 @ X1 @ X6))))),
% 0.61/0.41 inference(rectify,[],[f573])).
% 0.61/0.41 thf(f801,plain,(
% 0.61/0.41 ( ! [X0 : $tType] : ((id @ X0 = (^[Y0 : X0]: (Y0)))) )),
% 0.61/0.41 inference(cnf_transformation,[],[f519])).
% 0.61/0.41 thf(f830,plain,(
% 0.61/0.41 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X6 : X0,X4 : (X1 > X2),X5 : (X0 > X3)] : ((((sum_Inl @ X3 @ X2 @ (X5 @ X6))) = ((sum_map_sum @ X0 @ X3 @ X1 @ X2 @ X5 @ X4 @ (sum_Inl @ X0 @ X1 @ X6))))) )),
% 0.61/0.41 inference(cnf_transformation,[],[f733])).
% 0.61/0.41 thf(f834,plain,(
% 0.61/0.41 (t_tr = ((sum_Inl @ t @ dtree @ a)))),
% 0.61/0.41 inference(cnf_transformation,[],[f271])).
% 0.61/0.41 thf(f836,plain,(
% 0.61/0.41 (((sum_map_sum @ t @ t @ dtree @ n @ id @ t @ (comp @ n @ n @ dtree @ (comp @ dtree @ n @ n @ root @ (gram_L1451583624elle_H @ tr0)) @ root) @ t_tr)) != ((sum_map_sum @ t @ t @ dtree @ n @ id @ t @ root @ t_tr)))),
% 0.61/0.41 inference(cnf_transformation,[],[f569])).
% 0.61/0.41 thf(f866,plain,(
% 0.61/0.41 (((sum_map_sum @ t @ t @ dtree @ n @ (^[Y0 : t]: (Y0)) @ (comp @ n @ n @ dtree @ (comp @ dtree @ n @ n @ root @ (gram_L1451583624elle_H @ tr0)) @ root) @ t_tr)) != ((sum_map_sum @ t @ t @ dtree @ n @ (^[Y0 : t]: (Y0)) @ root @ t_tr)))),
% 0.61/0.41 inference(definition_unfolding,[],[f836,f801,f801])).
% 0.61/0.41 thf(f883,plain,(
% 0.61/0.41 (((sum_map_sum @ t @ t @ dtree @ n @ (^[Y0 : t]: (Y0)) @ (comp @ n @ n @ dtree @ (comp @ dtree @ n @ n @ root @ (gram_L1451583624elle_H @ tr0)) @ root) @ (sum_Inl @ t @ dtree @ a))) != ((sum_map_sum @ t @ t @ dtree @ n @ (^[Y0 : t]: (Y0)) @ root @ (sum_Inl @ t @ dtree @ a))))),
% 0.61/0.41 inference(forward_demodulation,[],[f866,f834])).
% 0.61/0.41 thf(f884,plain,(
% 0.61/0.41 (((sum_Inl @ t @ n @ ((^[Y0 : t]: (Y0)) @ a))) != ((sum_map_sum @ t @ t @ dtree @ n @ (^[Y0 : t]: (Y0)) @ (comp @ n @ n @ dtree @ (comp @ dtree @ n @ n @ root @ (gram_L1451583624elle_H @ tr0)) @ root) @ (sum_Inl @ t @ dtree @ a))))),
% 0.61/0.42 inference(forward_demodulation,[],[f883,f830])).
% 0.61/0.42 thf(f885,plain,(
% 0.61/0.42 (((sum_map_sum @ t @ t @ dtree @ n @ (^[Y0 : t]: (Y0)) @ (comp @ n @ n @ dtree @ (comp @ dtree @ n @ n @ root @ (gram_L1451583624elle_H @ tr0)) @ root) @ (sum_Inl @ t @ dtree @ a))) != ((sum_Inl @ t @ n @ a)))),
% 0.61/0.42 inference(beta-eta_normalization,[],[f884])).
% 0.61/0.42 thf(f886,plain,(
% 0.61/0.42 (((sum_Inl @ t @ n @ ((^[Y0 : t]: (Y0)) @ a))) != ((sum_Inl @ t @ n @ a)))),
% 0.61/0.42 inference(forward_demodulation,[],[f885,f830])).
% 0.61/0.42 thf(f887,plain,(
% 0.61/0.42 (((sum_Inl @ t @ n @ a)) != ((sum_Inl @ t @ n @ a)))),
% 0.61/0.42 inference(beta-eta_normalization,[],[f886])).
% 0.61/0.42 thf(f888,plain,(
% 0.61/0.42 $false),
% 0.61/0.42 inference(trivial_inequality_removal,[],[f887])).
% 0.61/0.42 % SZS output end Proof for theBenchmark
% 0.61/0.42 % (3499011)------------------------------
% 0.61/0.42 % (3499011)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.61/0.42 % (3499011)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.61/0.42 % (3499011)CaDiCaL version: 2.1.3
% 0.61/0.42 % (3499011)Termination reason: Refutation
% 0.61/0.42 % (3499011)Time elapsed: 0.020 s
% 0.61/0.42 % (3499011)Peak memory usage: 13 MB
% 0.61/0.42 % (3499011)Instructions burned: 72 (million)
% 0.61/0.42 % (3498976)Success in time 0.146 s
% 0.61/0.42 % Vampire exiting
%------------------------------------------------------------------------------