%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL011-1 : 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 : n019.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 09:37:37 AM UTC 2026
% Result : Unsatisfiable 6.08s 1.53s
% Output : Refutation 6.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 14 unt; 1 def)
% Number of atoms : 24 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 13 ~; 5 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : apply(apply(o,X0),X1) = apply(X1,apply(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',o_definition) ).
fof(f2,axiom,
! [X2,X0,X1] : apply(apply(apply(q1,X0),X1),X2) = apply(X0,apply(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',q1_definition) ).
fof(f3,negated_conjecture,
! [X0] : X0 != apply(combinator,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_fixed_point) ).
fof(f4,plain,
! [X0] : apply(combinator,X0) != X0,
inference(reorient_equations,[],[f3]) ).
fof(f5,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f6,plain,
! [X0,X1] : sQ0_eqProxy(apply(apply(o,X0),X1),apply(X1,apply(X0,X1))),
inference(equality_proxy_replacement,[],[f1,f5]) ).
fof(f7,plain,
! [X2,X0,X1] : sQ0_eqProxy(apply(apply(apply(q1,X0),X1),X2),apply(X0,apply(X2,X1))),
inference(equality_proxy_replacement,[],[f2,f5]) ).
fof(f8,plain,
! [X0] : ~ sQ0_eqProxy(apply(combinator,X0),X0),
inference(equality_proxy_replacement,[],[f4,f5]) ).
fof(f9,plain,
! [X2,X3,X0,X1] :
( ~ sQ0_eqProxy(X0,X1)
| ~ sQ0_eqProxy(X2,X3)
| sQ0_eqProxy(apply(X0,X2),apply(X1,X3)) ),
inference(equality_proxy_axiom,[],[f5]) ).
fof(f10,plain,
! [X0] : sQ0_eqProxy(X0,X0),
inference(equality_proxy_axiom,[],[f5]) ).
fof(f11,plain,
! [X0,X1] :
( ~ sQ0_eqProxy(X0,X1)
| sQ0_eqProxy(X1,X0) ),
inference(equality_proxy_axiom,[],[f5]) ).
fof(f12,plain,
! [X2,X0,X1] :
( ~ sQ0_eqProxy(X0,X1)
| ~ sQ0_eqProxy(X1,X2)
| sQ0_eqProxy(X0,X2) ),
inference(equality_proxy_axiom,[],[f5]) ).
fof(f13,plain,
! [X0] : ~ sQ0_eqProxy(X0,apply(combinator,X0)),
inference(forward_literal_rewriting,[],[f8,f11]) ).
fof(f20,plain,
! [X0,X1] : ~ sQ0_eqProxy(apply(X0,X1),apply(apply(apply(q1,combinator),X1),X0)),
inference(unit_resulting_resolution,[],[f12,f7,f13]) ).
fof(f38,plain,
! [X2,X0,X1] : ~ sQ0_eqProxy(apply(X0,apply(X1,X2)),apply(apply(apply(q1,combinator),X1),apply(apply(q1,X0),X2))),
inference(unit_resulting_resolution,[],[f12,f7,f20]) ).
fof(f170,plain,
! [X2,X0,X1] : ~ sQ0_eqProxy(apply(apply(X0,X1),X2),apply(apply(q1,apply(apply(apply(q1,apply(q1,combinator)),X1),X0)),X2)),
inference(unit_resulting_resolution,[],[f9,f7,f38]) ).
fof(f468,plain,
! [X0,X1] : ~ sQ0_eqProxy(apply(X0,X1),apply(q1,apply(apply(apply(q1,apply(q1,combinator)),X1),X0))),
inference(unit_resulting_resolution,[],[f9,f10,f170]) ).
fof(f853,plain,
$false,
inference(unit_resulting_resolution,[],[f12,f6,f7,f468]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL011-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n019.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Mon Sep 28 21:29:48 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running first-order theorem proving
% 0.09/0.21 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
% 6.08/1.53 % (295275)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.08/1.53 % (295280)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=1240686584:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 6.08/1.53 % (295284)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=492644410:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 6.08/1.53 % (295285)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=924824590:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 6.08/1.53 % (295286)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=526125861:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 6.08/1.53 % (295283)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3317738072:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 6.08/1.53 % (295282)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=1262594635:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 6.08/1.53 % (295281)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=3477751620:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 6.08/1.53 % (295283)Instruction limit reached!
% 6.08/1.53 % (295283)------------------------------
% 6.08/1.53 % (295283)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/1.53 % (295283)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/1.53 % (295283)CaDiCaL version: 2.1.3
% 6.08/1.53 % (295283)Termination reason: Instruction limit
% 6.08/1.53 % (295283)Termination phase: Saturation
% 6.08/1.53 % (295283)Time elapsed: 0.080 s
% 6.08/1.53 % (295283)Peak memory usage: 89 MB
% 6.08/1.53 % (295283)Instructions burned: 136 (million)
% 6.08/1.53 % (295284)Instruction limit reached!
% 6.08/1.53 % (295284)------------------------------
% 6.08/1.53 % (295284)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/1.53 % (295284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/1.53 % (295284)CaDiCaL version: 2.1.3
% 6.08/1.53 % (295284)Termination reason: Instruction limit
% 6.08/1.53 % (295284)Termination phase: Saturation
% 6.08/1.53 % (295284)Time elapsed: 0.100 s
% 6.08/1.53 % (295284)Peak memory usage: 88 MB
% 6.08/1.53 % (295284)Instructions burned: 181 (million)
% 6.08/1.53 % (295285)Instruction limit reached!
% 6.08/1.53 % (295285)------------------------------
% 6.08/1.53 % (295285)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/1.53 % (295285)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/1.53 % (295285)CaDiCaL version: 2.1.3
% 6.08/1.53 % (295285)Termination reason: Instruction limit
% 6.08/1.53 % (295285)Termination phase: Saturation
% 6.08/1.53 % (295285)Time elapsed: 0.161 s
% 6.08/1.53 % (295285)Peak memory usage: 90 MB
% 6.08/1.53 % (295285)Instructions burned: 258 (million)
% 6.08/1.53 % (295294)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3769908011:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2997 on theBenchmark for (2997ds/2051Mi)
% 6.08/1.53 % (295295)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=1398664801:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 6.08/1.53 % (295296)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3915842800:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 6.08/1.53 % (295296)First to succeed.
% 6.08/1.53 % (295296)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-295275"
% 6.08/1.53 % (295280)Also succeeded, but the first one will report.
% 6.08/1.53 % (295296)Refutation found. Thanks to Tanya!
% 6.08/1.53 % SZS status Unsatisfiable for theBenchmark
% 6.08/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 6.08/1.53 % (295296)------------------------------
% 6.08/1.53 % (295296)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.08/1.53 % (295296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.08/1.53 % (295296)CaDiCaL version: 2.1.3
% 6.08/1.53 % (295296)Termination reason: Refutation
% 6.08/1.53 % (295296)Time elapsed: 0.026 s
% 6.08/1.53 % (295296)Peak memory usage: 88 MB
% 6.08/1.53 % (295296)Instructions burned: 40 (million)
% 6.08/1.53 % (295296)------------------------------
% 6.08/1.53 % (295296)------------------------------
% 6.08/1.53 % (295275)Success in time 0.782 s
% 6.08/1.53 % Vampire exiting
%------------------------------------------------------------------------------