%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL044-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 09:37:43 AM UTC 2026
% Result : Unsatisfiable 6.10s 1.66s
% Output : Refutation 6.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 13 unt; 1 def)
% Number of atoms : 21 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 11 ~; 4 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
fof(f2,axiom,
! [X2,X0,X1] : apply(apply(apply(n,X0),X1),X2) = apply(apply(apply(X0,X2),X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_definition) ).
fof(f3,negated_conjecture,
! [X0] : apply(X0,f(X0)) != apply(f(X0),apply(X0,f(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_fixed_point) ).
fof(f4,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f5,plain,
! [X2,X0,X1] : sQ0_eqProxy(apply(apply(apply(b,X0),X1),X2),apply(X0,apply(X1,X2))),
inference(equality_proxy_replacement,[],[f1,f4]) ).
fof(f6,plain,
! [X2,X0,X1] : sQ0_eqProxy(apply(apply(apply(n,X0),X1),X2),apply(apply(apply(X0,X2),X1),X2)),
inference(equality_proxy_replacement,[],[f2,f4]) ).
fof(f7,plain,
! [X0] : ~ sQ0_eqProxy(apply(X0,f(X0)),apply(f(X0),apply(X0,f(X0)))),
inference(equality_proxy_replacement,[],[f3,f4]) ).
fof(f8,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,[],[f4]) ).
fof(f10,plain,
! [X0] : sQ0_eqProxy(X0,X0),
inference(equality_proxy_axiom,[],[f4]) ).
fof(f12,plain,
! [X2,X0,X1] :
( ~ sQ0_eqProxy(X0,X1)
| ~ sQ0_eqProxy(X1,X2)
| sQ0_eqProxy(X0,X2) ),
inference(equality_proxy_axiom,[],[f4]) ).
fof(f18,plain,
! [X0] : ~ sQ0_eqProxy(apply(X0,f(X0)),apply(apply(apply(b,f(X0)),X0),f(X0))),
inference(unit_resulting_resolution,[],[f12,f5,f7]) ).
fof(f26,plain,
! [X0] : ~ sQ0_eqProxy(apply(X0,f(X0)),apply(apply(apply(n,b),X0),f(X0))),
inference(unit_resulting_resolution,[],[f12,f6,f18]) ).
fof(f50,plain,
! [X0] : ~ sQ0_eqProxy(X0,apply(apply(n,b),X0)),
inference(unit_resulting_resolution,[],[f8,f10,f26]) ).
fof(f70,plain,
! [X0,X1] : ~ sQ0_eqProxy(apply(X0,X1),apply(apply(apply(b,apply(n,b)),X0),X1)),
inference(unit_resulting_resolution,[],[f12,f5,f50]) ).
fof(f113,plain,
! [X2,X0,X1] : ~ sQ0_eqProxy(apply(apply(apply(X0,X1),X2),X1),apply(apply(apply(b,apply(n,b)),apply(apply(n,X0),X2)),X1)),
inference(unit_resulting_resolution,[],[f12,f6,f70]) ).
fof(f604,plain,
$false,
inference(unit_resulting_resolution,[],[f8,f10,f5,f113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL044-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n016.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 21:35:34 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 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
% 6.10/1.66 % (4048249)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.10/1.66 % (4048264)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=1026523200:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 6.10/1.66 % (4048261)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=3242706399:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 6.10/1.66 % (4048263)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=3728497413:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 6.10/1.66 % (4048262)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=4188576203:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 6.10/1.66 % (4048260)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=2026231118:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 6.10/1.66 % (4048265)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=3218900873:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 6.10/1.66 % (4048266)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=1633306181:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 6.10/1.66 % (4048264)Instruction limit reached!
% 6.10/1.66 % (4048264)------------------------------
% 6.10/1.66 % (4048264)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/1.66 % (4048264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/1.66 % (4048264)CaDiCaL version: 2.1.3
% 6.10/1.66 % (4048264)Termination reason: Instruction limit
% 6.10/1.66 % (4048264)Termination phase: Saturation
% 6.10/1.66 % (4048264)Time elapsed: 0.058 s
% 6.10/1.66 % (4048264)Peak memory usage: 89 MB
% 6.10/1.66 % (4048264)Instructions burned: 184 (million)
% 6.10/1.66 % (4048263)Instruction limit reached!
% 6.10/1.66 % (4048263)------------------------------
% 6.10/1.66 % (4048263)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/1.66 % (4048263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/1.66 % (4048263)CaDiCaL version: 2.1.3
% 6.10/1.66 % (4048263)Termination reason: Instruction limit
% 6.10/1.66 % (4048263)Termination phase: Saturation
% 6.10/1.66 % (4048263)Time elapsed: 0.086 s
% 6.10/1.66 % (4048263)Peak memory usage: 89 MB
% 6.10/1.66 % (4048263)Instructions burned: 136 (million)
% 6.10/1.66 % (4048274)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=3971739161:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 6.10/1.66 % (4048265)Instruction limit reached!
% 6.10/1.66 % (4048265)------------------------------
% 6.10/1.66 % (4048265)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/1.66 % (4048265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/1.66 % (4048265)CaDiCaL version: 2.1.3
% 6.10/1.66 % (4048265)Termination reason: Instruction limit
% 6.10/1.66 % (4048265)Termination phase: Saturation
% 6.10/1.66 % (4048265)Time elapsed: 0.166 s
% 6.10/1.66 % (4048265)Peak memory usage: 91 MB
% 6.10/1.66 % (4048265)Instructions burned: 258 (million)
% 6.10/1.66 % (4048275)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3291105837:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 6.10/1.66 % (4048277)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=3802728713:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 6.10/1.66 % (4048277)First to succeed.
% 6.10/1.66 % (4048277)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4048249"
% 6.10/1.66 % (4048266)Also succeeded, but the first one will report.
% 6.10/1.66 % (4048274)Also succeeded, but the first one will report.
% 6.10/1.66 % (4048277)Refutation found. Thanks to Tanya!
% 6.10/1.66 % SZS status Unsatisfiable for theBenchmark
% 6.10/1.66 % SZS output start Proof for theBenchmark
% See solution above
% 6.10/1.66 % (4048277)------------------------------
% 6.10/1.66 % (4048277)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/1.66 % (4048277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/1.66 % (4048277)CaDiCaL version: 2.1.3
% 6.10/1.66 % (4048277)Termination reason: Refutation
% 6.10/1.66 % (4048277)Time elapsed: 0.023 s
% 6.10/1.66 % (4048277)Peak memory usage: 88 MB
% 6.10/1.66 % (4048277)Instructions burned: 36 (million)
% 6.10/1.66 % (4048277)------------------------------
% 6.10/1.66 % (4048277)------------------------------
% 6.10/1.66 % (4048249)Success in time 0.772 s
% 6.10/1.66 % Vampire exiting
%------------------------------------------------------------------------------