%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL078-2 : 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 : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:37:52 AM UTC 2026
% Result : Unsatisfiable 8.69s 2.06s
% Output : Refutation 8.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 17 unt; 0 def)
% Number of atoms : 25 ( 24 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 11 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : apply(k(X0),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',k_definition) ).
fof(f2,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(f3,axiom,
! [X0,X1] :
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
fof(f4,axiom,
! [X0] : apply(identity,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_definition) ).
fof(f5,negated_conjecture,
apply(apply(apply(abstraction,abstraction),abstraction),abstraction) != k(k(identity)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_TRC1b) ).
fof(f7,plain,
! [X2,X0,X1] : apply(apply(apply(abstraction,k(X0)),X1),X2) = apply(X0,apply(X1,X2)),
inference(superposition,[],[f2,f1]) ).
fof(f12,plain,
! [X2,X0,X1] : apply(X1,apply(apply(X0,X1),X2)) = apply(apply(apply(apply(abstraction,abstraction),X0),X1),X2),
inference(superposition,[],[f7,f2]) ).
fof(f19,plain,
apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity)))) != apply(k(k(identity)),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity)))),
inference(unit_resulting_resolution,[],[f3,f5]) ).
fof(f22,plain,
! [X0,X1] :
( apply(X1,n(k(X0),X1)) != X0
| k(X0) = X1 ),
inference(superposition,[],[f3,f1]) ).
fof(f26,plain,
! [X0] :
( n(X0,identity) != apply(X0,n(X0,identity))
| identity = X0 ),
inference(superposition,[],[f3,f4]) ).
fof(f28,plain,
k(identity) != apply(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity)))),
inference(forward_demodulation,[],[f19,f1]) ).
fof(f30,plain,
k(identity) != apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),
inference(forward_demodulation,[],[f28,f12]) ).
fof(f33,plain,
apply(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),n(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),k(identity))) != apply(k(identity),n(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),k(identity))),
inference(unit_resulting_resolution,[],[f3,f30]) ).
fof(f35,plain,
identity != apply(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),n(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),k(identity))),
inference(forward_demodulation,[],[f33,f1]) ).
fof(f44,plain,
! [X2,X0,X1] :
( apply(X0,apply(X1,n(k(X2),apply(apply(abstraction,k(X0)),X1)))) != X2
| k(X2) = apply(apply(abstraction,k(X0)),X1) ),
inference(superposition,[],[f22,f7]) ).
fof(f138,plain,
! [X0,X1] : k(X0) = apply(apply(abstraction,k(k(X0))),X1),
inference(unit_resulting_resolution,[],[f44,f1]) ).
fof(f170,plain,
! [X0,X1] : k(X0) = apply(apply(apply(abstraction,abstraction),X1),k(X0)),
inference(superposition,[],[f2,f138]) ).
fof(f408,plain,
! [X2,X0,X1] : apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X2),X0) = apply(k(X0),apply(X2,X0)),
inference(superposition,[],[f2,f170]) ).
fof(f412,plain,
! [X2,X0,X1] : apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),X1)),X2),X0) = X0,
inference(forward_demodulation,[],[f408,f1]) ).
fof(f1652,plain,
n(apply(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),n(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),k(identity))),identity) != apply(apply(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),n(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),k(identity))),n(apply(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),n(apply(abstraction,apply(apply(abstraction,abstraction),n(apply(apply(apply(abstraction,abstraction),abstraction),abstraction),k(k(identity))))),k(identity))),identity)),
inference(unit_resulting_resolution,[],[f26,f35]) ).
fof(f1656,plain,
$false,
inference(forward_subsumption_resolution,[],[f1652,f412]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL078-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 % Computer : n011.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Mon Sep 28 21:34:16 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.28 Running first-order theorem proving
% 0.10/0.28 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
% 6.97/1.85 % (3807844)Input is clausal, will run a generic CNF schedule.
% 6.97/1.85 % (3807849)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=816008083:i=140167_3000 on theBenchmark for (3000ds/140167Mi)
% 6.97/1.85 % (3807855)dis-21_1_sil=8000:lcm=predicate:random_seed=3233096081:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/117Mi)
% 6.97/1.85 % (3807855)Refutation not found, incomplete strategy
% 6.97/1.85 % (3807855)------------------------------
% 6.97/1.85 % (3807855)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.97/1.85 % (3807855)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.97/1.85 % (3807855)CaDiCaL version: 2.1.3
% 6.97/1.85 % (3807855)Termination reason: Refutation not found, incomplete strategy
% 6.97/1.85 % (3807855)Time elapsed: 0.002 s
% 6.97/1.85 % (3807855)Peak memory usage: 88 MB
% 6.97/1.85 % (3807850)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2445810046:i=132376:av=off_3000 on theBenchmark for (3000ds/132376Mi)
% 6.97/1.85 % (3807852)lrs+10_1_sil=8000:sp=occurrence:random_seed=1286536370:i=107:sd=3:ss=axioms:sgt=8_3000 on theBenchmark for (3000ds/107Mi)
% 6.97/1.85 % (3807854)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3378608652:s2a=on:i=180:gtg=position_3000 on theBenchmark for (3000ds/180Mi)
% 6.97/1.85 % (3807853)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3568614894:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_3000 on theBenchmark for (3000ds/114Mi)
% 6.97/1.85 % (3807851)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=60998596:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_3000 on theBenchmark for (3000ds/137899Mi)
% 6.97/1.85 % (3807852)Instruction limit reached!
% 6.97/1.85 % (3807852)------------------------------
% 6.97/1.85 % (3807852)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.97/1.85 % (3807852)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.97/1.85 % (3807852)CaDiCaL version: 2.1.3
% 6.97/1.85 % (3807852)Termination reason: Instruction limit
% 6.97/1.85 % (3807852)Termination phase: Saturation
% 6.97/1.85 % (3807852)Time elapsed: 0.108 s
% 6.97/1.85 % (3807852)Peak memory usage: 89 MB
% 6.97/1.85 % (3807852)Instructions burned: 107 (million)
% 6.97/1.85 % (3807853)Instruction limit reached!
% 6.97/1.85 % (3807853)------------------------------
% 6.97/1.85 % (3807853)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.97/1.85 % (3807853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.97/1.85 % (3807853)CaDiCaL version: 2.1.3
% 6.97/1.85 % (3807853)Termination reason: Instruction limit
% 6.97/1.85 % (3807853)Termination phase: Saturation
% 6.97/1.85 % (3807853)Time elapsed: 0.113 s
% 6.97/1.85 % (3807853)Peak memory usage: 89 MB
% 6.97/1.85 % (3807853)Instructions burned: 114 (million)
% 6.97/1.85 % (3807854)Instruction limit reached!
% 6.97/1.85 % (3807854)------------------------------
% 6.97/1.85 % (3807854)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.97/1.85 % (3807854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.97/1.85 % (3807854)CaDiCaL version: 2.1.3
% 6.97/1.85 % (3807854)Termination reason: Instruction limit
% 6.97/1.85 % (3807854)Termination phase: Saturation
% 6.97/1.85 % (3807854)Time elapsed: 0.169 s
% 6.97/1.85 % (3807854)Peak memory usage: 90 MB
% 6.97/1.85 % (3807854)Instructions burned: 181 (million)
% 6.97/1.85 % (3807863)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=776862422:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 6.97/1.85 % (3807863)Refutation not found, incomplete strategy
% 6.97/1.85 % (3807863)------------------------------
% 6.97/1.85 % (3807863)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.97/1.85 % (3807863)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.97/1.85 % (3807863)CaDiCaL version: 2.1.3
% 6.97/1.85 % (3807863)Termination reason: Refutation not found, incomplete strategy
% 6.97/1.85 % (3807863)Time elapsed: 0.002 s
% 6.97/1.85 % (3807863)Peak memory usage: 88 MB
% 6.97/1.85 % (3807855)------------------------------
% 6.97/1.85 % (3807855)------------------------------
% 6.97/1.85 % (3807864)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2702544681: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)
% 8.69/2.06 % (3807865)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1769643770:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 8.69/2.06 % (3807865)Refutation not found, incomplete strategy
% 8.69/2.06 % (3807865)------------------------------
% 8.69/2.06 % (3807865)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.69/2.06 % (3807865)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.69/2.06 % (3807865)CaDiCaL version: 2.1.3
% 8.69/2.06 % (3807865)Termination reason: Refutation not found, incomplete strategy
% 8.69/2.06 % (3807865)Time elapsed: 0.002 s
% 8.69/2.06 % (3807865)Peak memory usage: 88 MB
% 8.69/2.06 % (3807864)Instruction limit reached!
% 8.69/2.06 % (3807864)------------------------------
% 8.69/2.06 % (3807864)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.69/2.06 % (3807864)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.69/2.06 % (3807864)CaDiCaL version: 2.1.3
% 8.69/2.06 % (3807864)Termination reason: Instruction limit
% 8.69/2.06 % (3807864)Termination phase: Saturation
% 8.69/2.06 % (3807864)Time elapsed: 0.148 s
% 8.69/2.06 % (3807864)Peak memory usage: 96 MB
% 8.69/2.06 % (3807864)Instructions burned: 190 (million)
% 8.69/2.06 % (3807867)lrs+10_64_to=lpo:sil=8000:random_seed=2569488946:i=126:bd=preordered_2993 on theBenchmark for (2993ds/126Mi)
% 8.69/2.06 % (3807850)First to succeed.
% 8.69/2.06 % (3807850)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3807844"
% 8.69/2.06 % (3807863)------------------------------
% 8.69/2.06 % (3807863)------------------------------
% 8.69/2.06 % (3807867)Instruction limit reached!
% 8.69/2.06 % (3807867)------------------------------
% 8.69/2.06 % (3807867)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.69/2.06 % (3807867)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.69/2.06 % (3807867)CaDiCaL version: 2.1.3
% 8.69/2.06 % (3807867)Termination reason: Instruction limit
% 8.69/2.06 % (3807867)Termination phase: Saturation
% 8.69/2.06 % (3807867)Time elapsed: 0.125 s
% 8.69/2.06 % (3807867)Peak memory usage: 89 MB
% 8.69/2.06 % (3807867)Instructions burned: 126 (million)
% 8.69/2.06 % (3807870)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=3106649312:avsq=on:i=194:fgj=on:bd=preordered_2992 on theBenchmark for (2992ds/194Mi)
% 8.69/2.06 % (3807865)------------------------------
% 8.69/2.06 % (3807865)------------------------------
% 8.69/2.06 % (3807850)Refutation found. Thanks to Tanya!
% 8.69/2.06 % SZS status Unsatisfiable for theBenchmark
% 8.69/2.06 % SZS output start Proof for theBenchmark
% See solution above
% 8.69/2.06 % (3807850)------------------------------
% 8.69/2.06 % (3807850)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.69/2.06 % (3807850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.69/2.06 % (3807850)CaDiCaL version: 2.1.3
% 8.69/2.06 % (3807850)Termination reason: Refutation
% 8.69/2.06 % (3807850)Time elapsed: 0.644 s
% 8.69/2.06 % (3807850)Peak memory usage: 129 MB
% 8.69/2.06 % (3807850)Instructions burned: 1103 (million)
% 8.69/2.06 % (3807850)------------------------------
% 8.69/2.06 % (3807850)------------------------------
% 8.69/2.06 % (3807844)Success in time 1.129 s
% 8.69/2.06 % Vampire exiting
%------------------------------------------------------------------------------