%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL077-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 09:37:52 AM UTC 2026
% Result : Unsatisfiable 10.68s 2.47s
% Output : Refutation 10.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 29 unt; 5 def)
% Number of atoms : 35 ( 34 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 6 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 36 ( 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : apply(k(X0),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
fof(f6,axiom,
! [X2,X0,X1] : apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,k(X2)),apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',abstraction) ).
fof(f11,axiom,
! [X0,X1] :
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
fof(f13,axiom,
! [X0] : apply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_definition) ).
fof(f14,negated_conjecture,
apply(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),abstraction),abstraction) != identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_TRC1a) ).
fof(f15,plain,
identity != apply(apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),abstraction),abstraction),
inference(reorient_equations,[],[f14]) ).
fof(f16,definition,
sF0 = apply(abstraction,abstraction),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f17,plain,
apply(abstraction,abstraction) = sF0,
inference(reorient_equations,[],[f16]) ).
fof(f18,definition,
sF1 = apply(sF0,abstraction),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f19,plain,
apply(sF0,abstraction) = sF1,
inference(reorient_equations,[],[f18]) ).
fof(f20,definition,
sF2 = apply(sF1,abstraction),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f21,plain,
apply(sF1,abstraction) = sF2,
inference(reorient_equations,[],[f20]) ).
fof(f22,definition,
sF3 = apply(sF2,abstraction),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f23,plain,
apply(sF2,abstraction) = sF3,
inference(reorient_equations,[],[f22]) ).
fof(f24,definition,
sF4 = apply(sF3,abstraction),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
fof(f25,plain,
apply(sF3,abstraction) = sF4,
inference(reorient_equations,[],[f24]) ).
fof(f26,plain,
identity != sF4,
inference(definition_folding,[],[f15,f25,f23,f21,f19,f17]) ).
fof(f37,plain,
! [X0] :
( n(identity,X0) != apply(X0,n(identity,X0))
| identity = X0 ),
inference(superposition,[],[f11,f13]) ).
fof(f40,plain,
! [X2,X0,X1] : apply(apply(apply(abstraction,k(X0)),X1),X2) = apply(X0,apply(X1,X2)),
inference(superposition,[],[f6,f1]) ).
fof(f319,plain,
! [X2,X0,X1] : apply(X1,apply(apply(X0,X1),X2)) = apply(apply(apply(apply(abstraction,abstraction),X0),X1),X2),
inference(superposition,[],[f40,f6]) ).
fof(f358,plain,
! [X2,X0,X1] : apply(X1,apply(apply(X0,X1),X2)) = apply(apply(apply(sF0,X0),X1),X2),
inference(forward_demodulation,[],[f319,f17]) ).
fof(f395,plain,
! [X0,X1] : apply(X0,apply(apply(abstraction,X0),X1)) = apply(apply(sF1,X0),X1),
inference(superposition,[],[f358,f19]) ).
fof(f405,plain,
! [X2,X0,X1] : apply(apply(apply(sF0,X0),k(X1)),X2) = X1,
inference(superposition,[],[f1,f358]) ).
fof(f441,plain,
! [X0] : apply(apply(sF1,abstraction),X0) = apply(abstraction,apply(sF0,X0)),
inference(superposition,[],[f395,f17]) ).
fof(f502,plain,
! [X0] : apply(abstraction,apply(sF0,X0)) = apply(sF2,X0),
inference(forward_demodulation,[],[f441,f21]) ).
fof(f738,plain,
! [X2,X0,X1] : apply(apply(apply(abstraction,apply(sF0,X1)),X2),X0) = X0,
inference(superposition,[],[f6,f405]) ).
fof(f757,plain,
! [X2,X0,X1] : apply(apply(apply(sF2,X1),X2),X0) = X0,
inference(forward_demodulation,[],[f738,f502]) ).
fof(f797,plain,
! [X0,X1] :
( n(identity,apply(apply(sF2,X0),X1)) != n(identity,apply(apply(sF2,X0),X1))
| identity = apply(apply(sF2,X0),X1) ),
inference(superposition,[],[f37,f757]) ).
fof(f798,plain,
! [X0,X1] : identity = apply(apply(sF2,X0),X1),
inference(trivial_inequality_removal,[],[f797]) ).
fof(f827,plain,
! [X0] : identity = apply(sF3,X0),
inference(superposition,[],[f798,f23]) ).
fof(f863,plain,
identity = sF4,
inference(superposition,[],[f25,f827]) ).
fof(f898,plain,
$false,
inference(forward_subsumption_resolution,[],[f863,f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL077-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.25 % Computer : n014.cluster.edu
% 0.11/0.25 % Model : x86_64 x86_64
% 0.11/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.25 % Memory : 8046.5625MB
% 0.11/0.25 % OS : Linux 6.8.0-71-generic
% 0.11/0.25 % CPULimit : 300
% 0.11/0.26 % WCLimit : 300
% 0.11/0.26 % DateTime : Mon Sep 28 21:34:00 UTC 2026
% 0.11/0.26 % CPUTime :
% 0.11/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.32 Running first-order theorem proving
% 0.27/0.32 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
% 6.67/2.17 % (2212623)Input is clausal, will run a generic CNF schedule.
% 6.67/2.17 % (2212628)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=309099373:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 6.67/2.17 % (2212632)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1662583700:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 6.67/2.17 % (2212633)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2987400908:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 6.67/2.17 % (2212629)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3772320041:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 6.67/2.17 % (2212631)lrs+10_1_sil=8000:sp=occurrence:random_seed=3227821871:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 6.67/2.17 % (2212630)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=715198967:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 6.67/2.17 % (2212634)dis-21_1_sil=8000:lcm=predicate:random_seed=538778024:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 6.67/2.17 % (2212634)Refutation not found, incomplete strategy
% 6.67/2.17 % (2212634)------------------------------
% 6.67/2.17 % (2212634)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/2.17 % (2212634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/2.17 % (2212634)CaDiCaL version: 2.1.3
% 6.67/2.17 % (2212634)Termination reason: Refutation not found, incomplete strategy
% 6.67/2.17 % (2212634)Time elapsed: 0.002 s
% 6.67/2.17 % (2212634)Peak memory usage: 88 MB
% 6.67/2.17 % (2212632)Instruction limit reached!
% 6.67/2.17 % (2212632)------------------------------
% 6.67/2.17 % (2212632)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/2.17 % (2212632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/2.17 % (2212632)CaDiCaL version: 2.1.3
% 6.67/2.17 % (2212632)Termination reason: Instruction limit
% 6.67/2.17 % (2212632)Termination phase: Saturation
% 6.67/2.17 % (2212632)Time elapsed: 0.111 s
% 6.67/2.17 % (2212632)Peak memory usage: 89 MB
% 6.67/2.17 % (2212632)Instructions burned: 114 (million)
% 6.67/2.17 % (2212631)Instruction limit reached!
% 6.67/2.17 % (2212631)------------------------------
% 6.67/2.17 % (2212631)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/2.17 % (2212631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/2.17 % (2212631)CaDiCaL version: 2.1.3
% 6.67/2.17 % (2212631)Termination reason: Instruction limit
% 6.67/2.17 % (2212631)Termination phase: Saturation
% 6.67/2.17 % (2212631)Time elapsed: 0.109 s
% 6.67/2.17 % (2212631)Peak memory usage: 89 MB
% 6.67/2.17 % (2212631)Instructions burned: 107 (million)
% 6.67/2.17 % (2212633)Instruction limit reached!
% 6.67/2.17 % (2212633)------------------------------
% 6.67/2.17 % (2212633)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/2.17 % (2212633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/2.17 % (2212633)CaDiCaL version: 2.1.3
% 6.67/2.17 % (2212633)Termination reason: Instruction limit
% 6.67/2.17 % (2212633)Termination phase: Saturation
% 6.67/2.17 % (2212633)Time elapsed: 0.169 s
% 6.67/2.17 % (2212633)Peak memory usage: 90 MB
% 6.67/2.17 % (2212633)Instructions burned: 180 (million)
% 6.67/2.17 % (2212642)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=249461179:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 6.67/2.17 % (2212642)Refutation not found, incomplete strategy
% 6.67/2.17 % (2212642)------------------------------
% 6.67/2.17 % (2212642)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.67/2.17 % (2212642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.67/2.17 % (2212642)CaDiCaL version: 2.1.3
% 6.67/2.17 % (2212642)Termination reason: Refutation not found, incomplete strategy
% 6.67/2.17 % (2212642)Time elapsed: 0.002 s
% 6.67/2.17 % (2212642)Peak memory usage: 88 MB
% 6.67/2.17 % (2212643)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=394983752:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 10.68/2.47 % (2212634)------------------------------
% 10.68/2.47 % (2212634)------------------------------
% 10.68/2.47 % (2212644)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1402784214:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 10.68/2.47 % (2212644)Refutation not found, incomplete strategy
% 10.68/2.47 % (2212644)------------------------------
% 10.68/2.47 % (2212644)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.68/2.47 % (2212644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.68/2.47 % (2212644)CaDiCaL version: 2.1.3
% 10.68/2.47 % (2212644)Termination reason: Refutation not found, incomplete strategy
% 10.68/2.47 % (2212644)Time elapsed: 0.002 s
% 10.68/2.47 % (2212644)Peak memory usage: 88 MB
% 10.68/2.47 % (2212643)Instruction limit reached!
% 10.68/2.47 % (2212643)------------------------------
% 10.68/2.47 % (2212643)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.68/2.47 % (2212643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.68/2.47 % (2212643)CaDiCaL version: 2.1.3
% 10.68/2.47 % (2212643)Termination reason: Instruction limit
% 10.68/2.47 % (2212643)Termination phase: Saturation
% 10.68/2.47 % (2212643)Time elapsed: 0.177 s
% 10.68/2.47 % (2212643)Peak memory usage: 90 MB
% 10.68/2.47 % (2212643)Instructions burned: 190 (million)
% 10.68/2.47 % (2212648)lrs+10_64_to=lpo:sil=8000:random_seed=532621303:i=126:bd=preordered_2993 on theBenchmark for (2993ds/126Mi)
% 10.68/2.47 % (2212628)First to succeed.
% 10.68/2.47 % (2212628)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2212623"
% 10.68/2.47 % (2212648)Instruction limit reached!
% 10.68/2.47 % (2212648)------------------------------
% 10.68/2.47 % (2212648)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.68/2.47 % (2212648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.68/2.47 % (2212648)CaDiCaL version: 2.1.3
% 10.68/2.47 % (2212648)Termination reason: Instruction limit
% 10.68/2.47 % (2212648)Termination phase: Saturation
% 10.68/2.47 % (2212648)Time elapsed: 0.072 s
% 10.68/2.47 % (2212648)Peak memory usage: 89 MB
% 10.68/2.47 % (2212648)Instructions burned: 127 (million)
% 10.68/2.47 % (2212642)------------------------------
% 10.68/2.47 % (2212642)------------------------------
% 10.68/2.47 % (2212644)------------------------------
% 10.68/2.47 % (2212644)------------------------------
% 10.68/2.47 % (2212649)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3658979382:avsq=on:i=194:fgj=on:bd=preordered_2991 on theBenchmark for (2991ds/194Mi)
% 10.68/2.47 % (2212629)Also succeeded, but the first one will report.
% 10.68/2.47 % (2212649)Also succeeded, but the first one will report.
% 10.68/2.47 % (2212652)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=1590474355:i=157:gtg=all_2990 on theBenchmark for (2990ds/157Mi)
% 10.68/2.47 % (2212653)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=869342739:i=3394:sd=4:ss=included:sgt=64_2989 on theBenchmark for (2989ds/3394Mi)
% 10.68/2.47 % (2212654)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=2035980826:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2989 on theBenchmark for (2989ds/106Mi)
% 10.68/2.47 % (2212630)Also succeeded, but the first one will report.
% 10.68/2.47 % (2212654)Instruction limit reached!
% 10.68/2.47 % (2212654)------------------------------
% 10.68/2.47 % (2212654)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.68/2.47 % (2212654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.68/2.47 % (2212654)CaDiCaL version: 2.1.3
% 10.68/2.47 % (2212654)Termination reason: Instruction limit
% 10.68/2.47 % (2212654)Termination phase: Saturation
% 10.68/2.47 % (2212654)Time elapsed: 0.048 s
% 10.68/2.47 % (2212654)Peak memory usage: 89 MB
% 10.68/2.47 % (2212654)Instructions burned: 107 (million)
% 10.68/2.47 % (2212628)Refutation found. Thanks to Tanya!
% 10.68/2.47 % SZS status Unsatisfiable for theBenchmark
% 10.68/2.47 % SZS output start Proof for theBenchmark
% See solution above
% 10.68/2.47 % (2212628)------------------------------
% 10.68/2.47 % (2212628)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.68/2.47 % (2212628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.68/2.47 % (2212628)CaDiCaL version: 2.1.3
% 10.68/2.47 % (2212628)Termination reason: Refutation
% 10.68/2.47 % (2212628)Time elapsed: 0.780 s
% 10.68/2.47 % (2212628)Peak memory usage: 130 MB
% 10.68/2.47 % (2212628)Instructions burned: 1156 (million)
% 10.68/2.47 % (2212628)------------------------------
% 10.68/2.47 % (2212628)------------------------------
% 10.68/2.47 % (2212623)Success in time 1.402 s
% 10.68/2.47 % Vampire exiting
%------------------------------------------------------------------------------