%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL075-2 : 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 : 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 09:37:52 AM UTC 2026
% Result : Unsatisfiable 6.05s 1.92s
% Output : Refutation 6.05s
% 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 : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 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(f2,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(f3,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(f6,plain,
! [X2,X0,X1] : apply(apply(apply(k,X1),apply(k,X2)),apply(apply(X0,X1),X2)) = apply(apply(apply(apply(abstraction,abstraction),X0),X1),X2),
inference(superposition,[],[f2,f2]) ).
fof(f19,plain,
! [X2,X0,X1] : apply(apply(apply(apply(abstraction,abstraction),X0),X1),X2) = apply(X1,apply(apply(X0,X1),X2)),
inference(forward_demodulation,[],[f6,f1]) ).
fof(f108,plain,
! [X0] : apply(b(apply(apply(abstraction,abstraction),X0)),apply(apply(X0,b(apply(apply(abstraction,abstraction),X0))),c(apply(apply(abstraction,abstraction),X0)))) != apply(b(apply(apply(abstraction,abstraction),X0)),b(apply(apply(abstraction,abstraction),X0))),
inference(superposition,[],[f3,f19]) ).
fof(f446,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,[],[f108,f1]) ).
fof(f451,plain,
$false,
inference(trivial_inequality_removal,[],[f446]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL075-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 % Computer : n005.cluster.edu
% 0.09/0.24 % Model : x86_64 x86_64
% 0.09/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.24 % Memory : 8046.5625MB
% 0.09/0.24 % OS : Linux 6.8.0-71-generic
% 0.09/0.24 % CPULimit : 300
% 0.09/0.24 % WCLimit : 300
% 0.09/0.24 % DateTime : Mon Sep 28 21:33:46 UTC 2026
% 0.09/0.24 % CPUTime :
% 0.09/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.30 Running first-order theorem proving
% 0.23/0.30 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
% 6.05/1.91 % (1212462)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.05/1.91 % (1212474)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2896861348:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 6.05/1.91 % (1212469)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=1428164037:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 6.05/1.91 % (1212471)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1107100213:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 6.05/1.91 % (1212470)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=1288744974:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 6.05/1.92 % (1212473)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=2683987657:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 6.05/1.92 % (1212472)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3391580334:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 6.05/1.92 % (1212475)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2785497461:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 6.05/1.92 % (1212472)First to succeed.
% 6.05/1.92 % (1212472)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1212462"
% 6.05/1.92 % (1212475)Also succeeded, but the first one will report.
% 6.05/1.92 % (1212474)Instruction limit reached!
% 6.05/1.92 % (1212474)------------------------------
% 6.05/1.92 % (1212474)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.05/1.92 % (1212474)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.05/1.92 % (1212474)CaDiCaL version: 2.1.3
% 6.05/1.92 % (1212474)Termination reason: Instruction limit
% 6.05/1.92 % (1212474)Termination phase: Saturation
% 6.05/1.92 % (1212474)Time elapsed: 0.218 s
% 6.05/1.92 % (1212474)Peak memory usage: 90 MB
% 6.05/1.92 % (1212474)Instructions burned: 257 (million)
% 6.05/1.92 % (1212473)Instruction limit reached!
% 6.05/1.92 % (1212473)------------------------------
% 6.05/1.92 % (1212473)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.05/1.92 % (1212473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.05/1.92 % (1212473)CaDiCaL version: 2.1.3
% 6.05/1.92 % (1212473)Termination reason: Instruction limit
% 6.05/1.92 % (1212473)Termination phase: Saturation
% 6.05/1.92 % (1212473)Time elapsed: 0.172 s
% 6.05/1.92 % (1212473)Peak memory usage: 89 MB
% 6.05/1.92 % (1212473)Instructions burned: 181 (million)
% 6.05/1.92 % (1212485)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=1854162880:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2996 on theBenchmark for (2996ds/2051Mi)
% 6.05/1.92 % (1212472)Refutation found. Thanks to Tanya!
% 6.05/1.92 % SZS status Unsatisfiable for theBenchmark
% 6.05/1.92 % SZS output start Proof for theBenchmark
% See solution above
% 6.05/1.92 % (1212472)------------------------------
% 6.05/1.92 % (1212472)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.05/1.92 % (1212472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.05/1.92 % (1212472)CaDiCaL version: 2.1.3
% 6.05/1.92 % (1212472)Termination reason: Refutation
% 6.05/1.92 % (1212472)Time elapsed: 0.048 s
% 6.05/1.92 % (1212472)Peak memory usage: 88 MB
% 6.05/1.92 % (1212472)Instructions burned: 48 (million)
% 6.05/1.92 % (1212472)------------------------------
% 6.05/1.92 % (1212472)------------------------------
% 6.05/1.92 % (1212462)Success in time 0.717 s
% 6.05/1.92 % Vampire exiting
%------------------------------------------------------------------------------