%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL037-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 : Tue Sep 29 09:37:41 AM UTC 2026
% Result : Unsatisfiable 10.32s 2.22s
% Output : Refutation 10.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 10 unt; 0 def)
% Number of atoms : 10 ( 9 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_definition) ).
fof(f2,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
fof(f3,axiom,
! [X2,X0,X1] : apply(apply(apply(c,X0),X1),X2) = apply(apply(X0,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_definition) ).
fof(f4,negated_conjecture,
! [X0] : apply(X0,f(X0)) != apply(f(X0),apply(X0,f(X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_fixed_point) ).
fof(f13,plain,
! [X2,X0,X1] : apply(X1,apply(apply(X0,X1),X2)) = apply(apply(apply(apply(s,b),X0),X1),X2),
inference(superposition,[],[f2,f1]) ).
fof(f17,plain,
! [X2,X0,X1] : apply(apply(apply(s,apply(c,X0)),X1),X2) = apply(apply(X0,apply(X1,X2)),X2),
inference(superposition,[],[f1,f3]) ).
fof(f245,plain,
! [X2,X0,X1] : apply(apply(apply(apply(s,b),apply(c,X0)),X2),X1) = apply(X2,apply(apply(X0,X1),X2)),
inference(superposition,[],[f13,f3]) ).
fof(f720,plain,
! [X0,X1] : apply(apply(apply(apply(s,b),apply(c,X0)),f(apply(X0,X1))),X1) != apply(apply(X0,X1),f(apply(X0,X1))),
inference(superposition,[],[f4,f245]) ).
fof(f745,plain,
! [X2,X0,X1] : apply(apply(apply(apply(s,b),apply(c,apply(apply(s,apply(c,X0)),X1))),f(apply(apply(X0,apply(X1,X2)),X2))),X2) != apply(apply(apply(X0,apply(X1,X2)),X2),f(apply(apply(X0,apply(X1,X2)),X2))),
inference(superposition,[],[f720,f17]) ).
fof(f822,plain,
$false,
inference(unit_resulting_resolution,[],[f745,f3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL037-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n005.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Mon Sep 28 21:30:01 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running first-order theorem proving
% 0.08/0.20 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.32/2.22 % (1205407)Detected a unit-equality problem, will run specialized UEQ schedule.
% 10.32/2.22 % (1205520)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1815000859:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 10.32/2.22 % (1205517)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1278771424:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 10.32/2.22 % (1205518)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=2133105939:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 10.32/2.22 % (1205516)lrs+11_1_ncem=casc2026/models/loop6.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1346692778:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 10.32/2.22 % (1205515)lrs+1002_1_ncem=casc2026/models/loop7.pt:sil=128000:tgt=ground:npcc=on:drc=off:sp=reverse_frequency:spb=goal:acc=on:s2agt=16:kmz=on:sac=on:random_seed=1856103338:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 10.32/2.22 % (1205519)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3203534666:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 10.32/2.22 % (1205521)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1561666854:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 10.32/2.22 % (1205520)Instruction limit reached!
% 10.32/2.22 % (1205520)------------------------------
% 10.32/2.22 % (1205520)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.22 % (1205520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.22 % (1205520)CaDiCaL version: 2.1.3
% 10.32/2.22 % (1205520)Termination reason: Instruction limit
% 10.32/2.22 % (1205520)Termination phase: Saturation
% 10.32/2.22 % (1205520)Time elapsed: 0.126 s
% 10.32/2.22 % (1205520)Peak memory usage: 90 MB
% 10.32/2.22 % (1205520)Instructions burned: 260 (million)
% 10.32/2.22 % (1205518)Instruction limit reached!
% 10.32/2.22 % (1205518)------------------------------
% 10.32/2.22 % (1205518)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.22 % (1205518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.22 % (1205518)CaDiCaL version: 2.1.3
% 10.32/2.22 % (1205518)Termination reason: Instruction limit
% 10.32/2.22 % (1205518)Termination phase: Saturation
% 10.32/2.22 % (1205518)Time elapsed: 0.101 s
% 10.32/2.22 % (1205518)Peak memory usage: 89 MB
% 10.32/2.22 % (1205518)Instructions burned: 137 (million)
% 10.32/2.22 % (1205519)Instruction limit reached!
% 10.32/2.22 % (1205519)------------------------------
% 10.32/2.22 % (1205519)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.22 % (1205519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.22 % (1205519)CaDiCaL version: 2.1.3
% 10.32/2.22 % (1205519)Termination reason: Instruction limit
% 10.32/2.22 % (1205519)Termination phase: Saturation
% 10.32/2.22 % (1205519)Time elapsed: 0.148 s
% 10.32/2.22 % (1205519)Peak memory usage: 89 MB
% 10.32/2.22 % (1205519)Instructions burned: 181 (million)
% 10.32/2.22 % (1205571)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=79691998:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 10.32/2.22 % (1205572)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2061869706:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 10.32/2.22 % (1205573)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3396789054:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 10.32/2.22 % (1205573)Instruction limit reached!
% 10.32/2.22 % (1205573)------------------------------
% 10.32/2.22 % (1205573)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.22 % (1205573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.22 % (1205573)CaDiCaL version: 2.1.3
% 10.32/2.22 % (1205573)Termination reason: Instruction limit
% 10.32/2.22 % (1205573)Termination phase: Saturation
% 10.32/2.22 % (1205573)Time elapsed: 0.130 s
% 10.32/2.22 % (1205573)Peak memory usage: 90 MB
% 10.32/2.22 % (1205573)Instructions burned: 216 (million)
% 10.32/2.22 % (1205671)lrs+11_1_sil=16000:tgt=full:fde=none:sp=reverse_frequency:lma=off:fs=off:acc=on:bsr=unit_only:rp=on:random_seed=2918706824:avsq=on:i=317:avsqr=1,16:kws=arity_squared:add=off:fgj=on:ins=10:fsr=off:gtg=exists_sym_2993 on theBenchmark for (2993ds/317Mi)
% 10.32/2.22 % (1205521)Instruction limit reached!
% 10.32/2.22 % (1205521)------------------------------
% 10.32/2.22 % (1205521)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.22 % (1205521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.22 % (1205521)CaDiCaL version: 2.1.3
% 10.32/2.22 % (1205521)Termination reason: Instruction limit
% 10.32/2.22 % (1205521)Termination phase: Saturation
% 10.32/2.22 % (1205521)Time elapsed: 0.663 s
% 10.32/2.22 % (1205521)Peak memory usage: 100 MB
% 10.32/2.22 % (1205521)Instructions burned: 1187 (million)
% 10.32/2.22 % (1205671)Instruction limit reached!
% 10.32/2.22 % (1205671)------------------------------
% 10.32/2.22 % (1205671)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.22 % (1205671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.22 % (1205671)CaDiCaL version: 2.1.3
% 10.32/2.22 % (1205671)Termination reason: Instruction limit
% 10.32/2.22 % (1205671)Termination phase: Saturation
% 10.32/2.22 % (1205671)Time elapsed: 0.195 s
% 10.32/2.22 % (1205671)Peak memory usage: 94 MB
% 10.32/2.22 % (1205671)Instructions burned: 318 (million)
% 10.32/2.22 % (1205716)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=64000:tgt=full:npcc=on:sp=arity:lcm=predicate:urr=on:s2agt=16:br=off:random_seed=2681644746:i=12125:sd=2:fgj=on:ss=axioms:sgt=64_2991 on theBenchmark for (2991ds/12125Mi)
% 10.32/2.22 % (1205516)First to succeed.
% 10.32/2.22 % (1205516)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1205407"
% 10.32/2.22 % (1205732)lrs+10_32_sil=8000:tgt=ground:prc=on:sp=reverse_arity:spb=non_intro:random_seed=3353291710:i=2836:kws=inv_precedence:fgj=on:bd=preordered:ins=10_2989 on theBenchmark for (2989ds/2836Mi)
% 10.32/2.22 % (1205516)Refutation found. Thanks to Tanya!
% 10.32/2.22 % SZS status Unsatisfiable for theBenchmark
% 10.32/2.22 % SZS output start Proof for theBenchmark
% See solution above
% 10.32/2.22 % (1205516)------------------------------
% 10.32/2.22 % (1205516)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.32/2.22 % (1205516)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.32/2.22 % (1205516)CaDiCaL version: 2.1.3
% 10.32/2.22 % (1205516)Termination reason: Refutation
% 10.32/2.22 % (1205516)Time elapsed: 0.916 s
% 10.32/2.22 % (1205516)Peak memory usage: 133 MB
% 10.32/2.22 % (1205516)Instructions burned: 1449 (million)
% 10.32/2.22 % (1205516)------------------------------
% 10.32/2.22 % (1205516)------------------------------
% 10.32/2.22 % (1205407)Success in time 1.373 s
% 10.32/2.22 % Vampire exiting
%------------------------------------------------------------------------------