%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL066-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 09:37:50 AM UTC 2026
% Result : Unsatisfiable 2.82s 1.16s
% Output : Refutation 2.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 12 unt; 0 def)
% Number of atoms : 12 ( 11 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 10 ( 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X0,X1] : apply(apply(apply(q,X0),X1),X2) = apply(X1,apply(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',q_definition) ).
fof(f3,axiom,
! [X0,X1] : apply(apply(w,X0),X1) = apply(apply(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_definition) ).
fof(f4,negated_conjecture,
apply(apply(apply(apply(apply(apply(q,q),apply(w,apply(q,apply(q,q)))),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p_combinator) ).
fof(f29,plain,
! [X0,X1] : apply(apply(w,apply(q,X0)),X1) = apply(X1,apply(X0,X1)),
inference(superposition,[],[f2,f3]) ).
fof(f34,plain,
apply(apply(x,y),apply(apply(x,y),z)) != apply(apply(apply(apply(apply(w,apply(q,apply(q,q))),apply(q,x)),y),y),z),
inference(superposition,[],[f4,f2]) ).
fof(f35,plain,
! [X2,X0,X1] : apply(apply(X0,apply(X1,X2)),X2) = apply(apply(w,apply(apply(q,X1),X0)),X2),
inference(superposition,[],[f3,f2]) ).
fof(f37,plain,
apply(apply(x,y),apply(apply(x,y),z)) != apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z),
inference(forward_demodulation,[],[f34,f3]) ).
fof(f178,plain,
apply(apply(x,y),apply(apply(x,y),z)) != apply(apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y),z),
inference(superposition,[],[f37,f29]) ).
fof(f712,plain,
apply(apply(x,y),apply(apply(x,y),z)) != apply(apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y),z),
inference(superposition,[],[f178,f35]) ).
fof(f724,plain,
apply(apply(x,y),apply(apply(x,y),z)) != apply(apply(apply(apply(q,x),apply(q,apply(x,y))),y),z),
inference(forward_demodulation,[],[f712,f2]) ).
fof(f740,plain,
apply(apply(x,y),apply(apply(x,y),z)) != apply(apply(apply(q,apply(x,y)),apply(x,y)),z),
inference(forward_demodulation,[],[f724,f2]) ).
fof(f746,plain,
$false,
inference(forward_subsumption_resolution,[],[f740,f2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL066-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n016.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 21:38:24 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running first-order theorem proving
% 0.09/0.22 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
% 2.82/1.16 % (4051821)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.82/1.16 % (4051832)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=3088626504:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.82/1.16 % (4051832)First to succeed.
% 2.82/1.16 % (4051832)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4051821"
% 2.82/1.16 % (4051831)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3819299961:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.82/1.16 % (4051827)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=909938966:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.82/1.16 % (4051829)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=866921005:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.82/1.16 % (4051826)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=3678019867:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.82/1.16 % (4051830)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=183280229:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.82/1.16 % (4051828)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=318226026:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.82/1.16 % (4051829)Also succeeded, but the first one will report.
% 2.82/1.16 % (4051831)Also succeeded, but the first one will report.
% 2.82/1.16 % (4051830)Instruction limit reached!
% 2.82/1.16 % (4051830)------------------------------
% 2.82/1.16 % (4051830)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.16 % (4051830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.16 % (4051830)CaDiCaL version: 2.1.3
% 2.82/1.16 % (4051830)Termination reason: Instruction limit
% 2.82/1.16 % (4051830)Termination phase: Saturation
% 2.82/1.16 % (4051830)Time elapsed: 0.101 s
% 2.82/1.16 % (4051830)Peak memory usage: 89 MB
% 2.82/1.16 % (4051830)Instructions burned: 182 (million)
% 2.82/1.16 % (4051832)Refutation found. Thanks to Tanya!
% 2.82/1.16 % SZS status Unsatisfiable for theBenchmark
% 2.82/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.82/1.16 % (4051832)------------------------------
% 2.82/1.16 % (4051832)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.82/1.16 % (4051832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.82/1.16 % (4051832)CaDiCaL version: 2.1.3
% 2.82/1.16 % (4051832)Termination reason: Refutation
% 2.82/1.16 % (4051832)Time elapsed: 0.015 s
% 2.82/1.16 % (4051832)Peak memory usage: 88 MB
% 2.82/1.16 % (4051832)Instructions burned: 49 (million)
% 2.82/1.16 % (4051832)------------------------------
% 2.82/1.16 % (4051832)------------------------------
% 2.82/1.16 % (4051821)Success in time 0.308 s
% 2.82/1.16 % Vampire exiting
%------------------------------------------------------------------------------