%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL061-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 09:37:47 AM UTC 2026
% Result : Unsatisfiable 3.72s 1.26s
% Output : Refutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 10 unt; 0 def)
% Number of atoms : 10 ( 9 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
fof(f2,axiom,
! [X0,X1] : apply(apply(t,X0),X1) = apply(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t_definition) ).
fof(f3,negated_conjecture,
! [X0] : apply(apply(apply(X0,f(X0)),g(X0)),h(X0)) != apply(f(X0),apply(h(X0),g(X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_q1_combinator) ).
fof(f8,plain,
! [X0,X1] : apply(f(apply(apply(b,X0),X1)),apply(h(apply(apply(b,X0),X1)),g(apply(apply(b,X0),X1)))) != apply(apply(apply(X0,apply(X1,f(apply(apply(b,X0),X1)))),g(apply(apply(b,X0),X1))),h(apply(apply(b,X0),X1))),
inference(superposition,[],[f3,f1]) ).
fof(f15,plain,
! [X0,X1] : apply(f(apply(apply(b,apply(t,X1)),X0)),apply(h(apply(apply(b,apply(t,X1)),X0)),g(apply(apply(b,apply(t,X1)),X0)))) != apply(apply(apply(apply(X0,f(apply(apply(b,apply(t,X1)),X0))),X1),g(apply(apply(b,apply(t,X1)),X0))),h(apply(apply(b,apply(t,X1)),X0))),
inference(superposition,[],[f8,f2]) ).
fof(f44,plain,
! [X2,X0,X1] : apply(f(apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1))),apply(h(apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1))),g(apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1))))) != apply(apply(apply(apply(X0,apply(X1,f(apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1))))),X2),g(apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1)))),h(apply(apply(b,apply(t,X2)),apply(apply(b,X0),X1)))),
inference(superposition,[],[f15,f1]) ).
fof(f257,plain,
! [X0,X1] : apply(f(apply(apply(b,apply(t,X1)),apply(apply(b,b),X0))),apply(h(apply(apply(b,apply(t,X1)),apply(apply(b,b),X0))),g(apply(apply(b,apply(t,X1)),apply(apply(b,b),X0))))) != apply(apply(apply(X0,f(apply(apply(b,apply(t,X1)),apply(apply(b,b),X0)))),apply(X1,g(apply(apply(b,apply(t,X1)),apply(apply(b,b),X0))))),h(apply(apply(b,apply(t,X1)),apply(apply(b,b),X0)))),
inference(superposition,[],[f44,f1]) ).
fof(f430,plain,
! [X0] : apply(f(apply(apply(b,apply(t,X0)),apply(apply(b,b),b))),apply(apply(X0,g(apply(apply(b,apply(t,X0)),apply(apply(b,b),b)))),h(apply(apply(b,apply(t,X0)),apply(apply(b,b),b))))) != apply(f(apply(apply(b,apply(t,X0)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,X0)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,X0)),apply(apply(b,b),b))))),
inference(superposition,[],[f257,f1]) ).
fof(f447,plain,
apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))) != apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))),
inference(superposition,[],[f430,f2]) ).
fof(f449,plain,
$false,
inference(trivial_inequality_removal,[],[f447]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL061-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 % Computer : n001.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Mon Sep 28 21:38:15 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 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
% 3.72/1.26 % (779010)Detected a unit-equality problem, will run specialized UEQ schedule.
% 3.72/1.26 % (779071)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2083957102:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_3000 on theBenchmark for (3000ds/130716Mi)
% 3.72/1.26 % (779078)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=709585831:i=1187:sd=4:av=off:ss=axioms:sgt=32_3000 on theBenchmark for (3000ds/1187Mi)
% 3.72/1.26 % (779073)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3686411682:i=136:bd=preordered:ins=2:av=off_3000 on theBenchmark for (3000ds/136Mi)
% 3.72/1.26 % (779075)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3055813040:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_3000 on theBenchmark for (3000ds/181Mi)
% 3.72/1.26 % (779070)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=3726216054:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/130792Mi)
% 3.72/1.26 % (779069)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=1913247907:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_3000 on theBenchmark for (3000ds/138329Mi)
% 3.72/1.26 % (779076)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2713024384:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_3000 on theBenchmark for (3000ds/257Mi)
% 3.72/1.26 % (779078)First to succeed.
% 3.72/1.26 % (779078)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-779010"
% 3.72/1.26 % (779073)Instruction limit reached!
% 3.72/1.26 % (779073)------------------------------
% 3.72/1.26 % (779073)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.26 % (779073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.26 % (779073)CaDiCaL version: 2.1.3
% 3.72/1.26 % (779073)Termination reason: Instruction limit
% 3.72/1.26 % (779073)Termination phase: Saturation
% 3.72/1.26 % (779073)Time elapsed: 0.080 s
% 3.72/1.26 % (779073)Peak memory usage: 89 MB
% 3.72/1.26 % (779073)Instructions burned: 136 (million)
% 3.72/1.26 % (779075)Instruction limit reached!
% 3.72/1.26 % (779075)------------------------------
% 3.72/1.26 % (779075)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.26 % (779075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.26 % (779075)CaDiCaL version: 2.1.3
% 3.72/1.26 % (779075)Termination reason: Instruction limit
% 3.72/1.26 % (779075)Termination phase: Saturation
% 3.72/1.26 % (779075)Time elapsed: 0.093 s
% 3.72/1.26 % (779075)Peak memory usage: 88 MB
% 3.72/1.26 % (779075)Instructions burned: 182 (million)
% 3.72/1.26 % (779076)Instruction limit reached!
% 3.72/1.26 % (779076)------------------------------
% 3.72/1.26 % (779076)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.26 % (779076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.26 % (779076)CaDiCaL version: 2.1.3
% 3.72/1.26 % (779076)Termination reason: Instruction limit
% 3.72/1.26 % (779076)Termination phase: Saturation
% 3.72/1.26 % (779076)Time elapsed: 0.152 s
% 3.72/1.26 % (779076)Peak memory usage: 90 MB
% 3.72/1.26 % (779076)Instructions burned: 258 (million)
% 3.72/1.26 % (779135)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2309777888:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 3.72/1.26 % (779136)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=867723852:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 3.72/1.26 % (779142)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=1393286650:i=215:ep=RSTC_2997 on theBenchmark for (2997ds/215Mi)
% 3.72/1.26 % (779078)Refutation found. Thanks to Tanya!
% 3.72/1.26 % SZS status Unsatisfiable for theBenchmark
% 3.72/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.72/1.26 % (779078)------------------------------
% 3.72/1.26 % (779078)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.26 % (779078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.26 % (779078)CaDiCaL version: 2.1.3
% 3.72/1.26 % (779078)Termination reason: Refutation
% 3.72/1.26 % (779078)Time elapsed: 0.047 s
% 3.72/1.26 % (779078)Peak memory usage: 88 MB
% 3.72/1.26 % (779078)Instructions burned: 82 (million)
% 3.72/1.26 % (779078)------------------------------
% 3.72/1.26 % (779078)------------------------------
% 3.72/1.26 % (779010)Success in time 0.435 s
% 3.72/1.26 % Vampire exiting
%------------------------------------------------------------------------------