%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL075-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 09:37:51 AM UTC 2026
% Result : Unsatisfiable 4.07s 1.26s
% Output : Refutation 4.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 8 unt; 0 def)
% Number of atoms : 8 ( 7 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 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 : 13 ( 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : apply(apply(k,X0),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_definition) ).
fof(f6,axiom,
! [X2,X0,X1] : apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,apply(k,X2)),apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abstraction) ).
fof(f13,negated_conjecture,
! [X0] : apply(apply(X0,b(X0)),c(X0)) != apply(b(X0),b(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_diagonal_combinator) ).
fof(f68,plain,
! [X2,X0,X1] : apply(apply(apply(abstraction,X1),apply(k,X0)),X2) = apply(apply(X1,apply(k,X2)),X0),
inference(superposition,[],[f6,f1]) ).
fof(f463,plain,
! [X0,X1] : apply(apply(apply(k,X0),apply(k,X1)),X0) = apply(apply(apply(apply(abstraction,abstraction),k),X0),X1),
inference(superposition,[],[f68,f6]) ).
fof(f492,plain,
! [X0,X1] : apply(apply(apply(apply(abstraction,abstraction),k),X0),X1) = apply(X0,X0),
inference(forward_demodulation,[],[f463,f1]) ).
fof(f2462,plain,
apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))) != apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))),
inference(superposition,[],[f13,f492]) ).
fof(f2578,plain,
$false,
inference(trivial_inequality_removal,[],[f2462]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL075-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n002.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 21:36:33 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.07/1.26 % (798910)Input is clausal, will run a generic CNF schedule.
% 4.07/1.26 % (798915)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=2369477859:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.07/1.26 % (798920)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3916612745:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.07/1.26 % (798918)lrs+10_1_sil=8000:sp=occurrence:random_seed=2620426273:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.07/1.26 % (798916)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1071431152:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.07/1.26 % (798919)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3737433338:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.07/1.26 % (798917)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1629051522:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.07/1.26 % (798921)dis-21_1_sil=8000:lcm=predicate:random_seed=40102403: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)
% 4.07/1.26 % (798918)Refutation not found, incomplete strategy
% 4.07/1.26 % (798918)------------------------------
% 4.07/1.26 % (798918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.07/1.26 % (798919)Refutation not found, incomplete strategy
% 4.07/1.26 % (798919)------------------------------
% 4.07/1.26 % (798919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.07/1.26 % (798919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.07/1.26 % (798918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.07/1.26 % (798919)CaDiCaL version: 2.1.3
% 4.07/1.26 % (798918)CaDiCaL version: 2.1.3
% 4.07/1.26 % (798919)Termination reason: Refutation not found, incomplete strategy
% 4.07/1.26 % (798919)Time elapsed: 0.001 s
% 4.07/1.26 % (798918)Termination reason: Refutation not found, incomplete strategy
% 4.07/1.26 % (798918)Time elapsed: 0.001 s
% 4.07/1.26 % (798919)Peak memory usage: 87 MB
% 4.07/1.26 % (798918)Peak memory usage: 87 MB
% 4.07/1.26 % (798921)Refutation not found, incomplete strategy
% 4.07/1.26 % (798921)------------------------------
% 4.07/1.26 % (798921)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.07/1.26 % (798921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.07/1.26 % (798921)CaDiCaL version: 2.1.3
% 4.07/1.26 % (798921)Termination reason: Refutation not found, incomplete strategy
% 4.07/1.26 % (798921)Time elapsed: 0.001 s
% 4.07/1.26 % (798921)Peak memory usage: 88 MB
% 4.07/1.26 % (798920)First to succeed.
% 4.07/1.26 % (798920)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-798910"
% 4.07/1.26 % (798921)------------------------------
% 4.07/1.26 % (798921)------------------------------
% 4.07/1.26 % (798919)------------------------------
% 4.07/1.26 % (798919)------------------------------
% 4.07/1.26 % (798918)------------------------------
% 4.07/1.26 % (798918)------------------------------
% 4.07/1.26 % (798920)Refutation found. Thanks to Tanya!
% 4.07/1.26 % SZS status Unsatisfiable for theBenchmark
% 4.07/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 4.07/1.26 % (798920)------------------------------
% 4.07/1.26 % (798920)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.07/1.26 % (798920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.07/1.26 % (798920)CaDiCaL version: 2.1.3
% 4.07/1.26 % (798920)Termination reason: Refutation
% 4.07/1.26 % (798920)Time elapsed: 0.098 s
% 4.07/1.26 % (798920)Peak memory usage: 90 MB
% 4.07/1.26 % (798920)Instructions burned: 162 (million)
% 4.07/1.26 % (798920)------------------------------
% 4.07/1.26 % (798920)------------------------------
% 4.07/1.26 % (798910)Success in time 0.503 s
% 4.07/1.26 % Vampire exiting
%------------------------------------------------------------------------------