%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : COL002-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 09:37:32 AM UTC 2026
% Result : Unsatisfiable 6.16s 1.67s
% Output : Refutation 6.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 24 unt; 1 def)
% Number of atoms : 39 ( 9 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 30 ( 20 ~; 9 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-4 aty)
% Number of variables : 61 ( 61 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s_definition) ).
fof(f3,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(f5,axiom,
! [X0] : apply(i,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i_definition) ).
fof(f6,axiom,
! [X0] : ifeq(X0,apply(fixed_pt,X0),fixed_point(X0),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',weak_fixed_point) ).
fof(f7,plain,
! [X0] : true = ifeq(X0,apply(fixed_pt,X0),fixed_point(X0),true),
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
! [X0] : fixed_point(apply(apply(apply(s,apply(b,X0)),i),apply(apply(s,apply(b,X0)),i))) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_weak_fixed_point) ).
fof(f9,plain,
! [X0] : true != fixed_point(apply(apply(apply(s,apply(b,X0)),i),apply(apply(s,apply(b,X0)),i))),
inference(reorient_equations,[],[f8]) ).
fof(f10,definition,
! [X0,X1] :
( sQ0_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
fof(f11,plain,
! [X2,X0,X1] : sQ0_eqProxy(ifeq(X0,X0,X1,X2),X1),
inference(equality_proxy_replacement,[],[f1,f10]) ).
fof(f12,plain,
! [X2,X0,X1] : sQ0_eqProxy(apply(apply(apply(s,X0),X1),X2),apply(apply(X0,X2),apply(X1,X2))),
inference(equality_proxy_replacement,[],[f2,f10]) ).
fof(f13,plain,
! [X2,X0,X1] : sQ0_eqProxy(apply(apply(apply(b,X0),X1),X2),apply(X0,apply(X1,X2))),
inference(equality_proxy_replacement,[],[f3,f10]) ).
fof(f15,plain,
! [X0] : sQ0_eqProxy(apply(i,X0),X0),
inference(equality_proxy_replacement,[],[f5,f10]) ).
fof(f16,plain,
! [X0] : sQ0_eqProxy(true,ifeq(X0,apply(fixed_pt,X0),fixed_point(X0),true)),
inference(equality_proxy_replacement,[],[f7,f10]) ).
fof(f17,plain,
! [X0] : ~ sQ0_eqProxy(true,fixed_point(apply(apply(apply(s,apply(b,X0)),i),apply(apply(s,apply(b,X0)),i)))),
inference(equality_proxy_replacement,[],[f9,f10]) ).
fof(f18,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ sQ0_eqProxy(X0,X1)
| ~ sQ0_eqProxy(X2,X3)
| ~ sQ0_eqProxy(X4,X5)
| ~ sQ0_eqProxy(X6,X7)
| sQ0_eqProxy(ifeq(X0,X2,X4,X6),ifeq(X1,X3,X5,X7)) ),
inference(equality_proxy_axiom,[],[f10]) ).
fof(f19,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,[],[f10]) ).
fof(f21,plain,
! [X0] : sQ0_eqProxy(X0,X0),
inference(equality_proxy_axiom,[],[f10]) ).
fof(f22,plain,
! [X0,X1] :
( ~ sQ0_eqProxy(X0,X1)
| sQ0_eqProxy(X1,X0) ),
inference(equality_proxy_axiom,[],[f10]) ).
fof(f23,plain,
! [X2,X0,X1] :
( ~ sQ0_eqProxy(X0,X1)
| ~ sQ0_eqProxy(X1,X2)
| sQ0_eqProxy(X0,X2) ),
inference(equality_proxy_axiom,[],[f10]) ).
fof(f28,plain,
! [X2,X0,X1] : ~ sQ0_eqProxy(true,ifeq(X0,X0,fixed_point(apply(apply(apply(s,apply(b,X1)),i),apply(apply(s,apply(b,X1)),i))),X2)),
inference(unit_resulting_resolution,[],[f23,f11,f17]) ).
fof(f39,plain,
! [X2,X3,X0,X1] : ~ sQ0_eqProxy(ifeq(X0,apply(fixed_pt,X0),fixed_point(X0),true),ifeq(X1,X1,fixed_point(apply(apply(apply(s,apply(b,X2)),i),apply(apply(s,apply(b,X2)),i))),X3)),
inference(unit_resulting_resolution,[],[f23,f16,f28]) ).
fof(f105,plain,
! [X2,X3,X0,X1] : ~ sQ0_eqProxy(ifeq(X0,X0,fixed_point(apply(apply(apply(s,apply(b,X1)),i),apply(apply(s,apply(b,X1)),i))),X2),ifeq(X3,apply(fixed_pt,X3),fixed_point(X3),true)),
inference(unit_resulting_resolution,[],[f22,f39]) ).
fof(f219,plain,
! [X0] : ~ sQ0_eqProxy(apply(apply(apply(b,fixed_pt),apply(apply(s,apply(b,X0)),i)),apply(apply(s,apply(b,X0)),i)),apply(apply(apply(s,apply(b,X0)),i),apply(apply(s,apply(b,X0)),i))),
inference(unit_resulting_resolution,[],[f18,f21,f13,f21,f105]) ).
fof(f247,plain,
! [X0] : ~ sQ0_eqProxy(apply(apply(apply(s,apply(b,X0)),i),apply(apply(s,apply(b,X0)),i)),apply(apply(apply(b,fixed_pt),apply(apply(s,apply(b,X0)),i)),apply(apply(s,apply(b,X0)),i))),
inference(forward_literal_rewriting,[],[f219,f22]) ).
fof(f816,plain,
! [X0] : ~ sQ0_eqProxy(apply(apply(apply(b,X0),apply(apply(s,apply(b,X0)),i)),apply(i,apply(apply(s,apply(b,X0)),i))),apply(apply(apply(b,fixed_pt),apply(apply(s,apply(b,X0)),i)),apply(apply(s,apply(b,X0)),i))),
inference(unit_resulting_resolution,[],[f23,f12,f247]) ).
fof(f824,plain,
! [X0] : ~ sQ0_eqProxy(apply(apply(apply(b,fixed_pt),apply(apply(s,apply(b,X0)),i)),apply(apply(s,apply(b,X0)),i)),apply(apply(apply(b,X0),apply(apply(s,apply(b,X0)),i)),apply(i,apply(apply(s,apply(b,X0)),i)))),
inference(forward_literal_rewriting,[],[f816,f22]) ).
fof(f2194,plain,
~ sQ0_eqProxy(apply(apply(s,apply(b,fixed_pt)),i),apply(i,apply(apply(s,apply(b,fixed_pt)),i))),
inference(unit_resulting_resolution,[],[f19,f21,f824]) ).
fof(f2361,plain,
$false,
inference(unit_resulting_resolution,[],[f22,f15,f2194]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL002-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n008.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 21:29:09 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 6.16/1.67 % (2670356)Detected a unit-equality problem, will run specialized UEQ schedule.
% 6.16/1.67 % (2670505)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=752659495:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 6.16/1.67 % (2670503)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=1700502463:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 6.16/1.67 % (2670507)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=1577073107:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 6.16/1.67 % (2670497)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=853541277:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 6.16/1.67 % (2670501)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2505707599:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 6.16/1.67 % (2670509)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2067597755:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 6.16/1.67 % (2670499)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=4143451567:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 6.16/1.67 % (2670505)Instruction limit reached!
% 6.16/1.67 % (2670505)------------------------------
% 6.16/1.67 % (2670505)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.16/1.67 % (2670505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.16/1.67 % (2670505)CaDiCaL version: 2.1.3
% 6.16/1.67 % (2670505)Termination reason: Instruction limit
% 6.16/1.67 % (2670505)Termination phase: Saturation
% 6.16/1.67 % (2670505)Time elapsed: 0.050 s
% 6.16/1.67 % (2670505)Peak memory usage: 88 MB
% 6.16/1.67 % (2670505)Instructions burned: 182 (million)
% 6.16/1.67 % (2670503)Instruction limit reached!
% 6.16/1.67 % (2670503)------------------------------
% 6.16/1.67 % (2670503)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.16/1.67 % (2670503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.16/1.67 % (2670503)CaDiCaL version: 2.1.3
% 6.16/1.67 % (2670503)Termination reason: Instruction limit
% 6.16/1.67 % (2670503)Termination phase: Saturation
% 6.16/1.67 % (2670503)Time elapsed: 0.078 s
% 6.16/1.67 % (2670503)Peak memory usage: 88 MB
% 6.16/1.67 % (2670503)Instructions burned: 137 (million)
% 6.16/1.67 % (2670527)lrs-1011_1_ncem=casc2026/models/loop8.pt:sil=32000:npcc=on:prc=on:fde=unused:lcm=predicate:bsr=on:flr=on:random_seed=2927179876:i=2051:gtgl=2:fgj=on:bd=all:gtg=exists_top_2998 on theBenchmark for (2998ds/2051Mi)
% 6.16/1.67 % (2670507)Instruction limit reached!
% 6.16/1.67 % (2670507)------------------------------
% 6.16/1.67 % (2670507)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.16/1.67 % (2670507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.16/1.67 % (2670507)CaDiCaL version: 2.1.3
% 6.16/1.67 % (2670507)Termination reason: Instruction limit
% 6.16/1.67 % (2670507)Termination phase: Saturation
% 6.16/1.67 % (2670507)Time elapsed: 0.158 s
% 6.16/1.67 % (2670507)Peak memory usage: 90 MB
% 6.16/1.67 % (2670507)Instructions burned: 258 (million)
% 6.16/1.67 % (2670528)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=3896261920:i=4948:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/4948Mi)
% 6.16/1.67 % (2670530)lrs+10_5:1_sil=8000:sos=all:urr=on:br=off:flr=on:random_seed=241853954:i=215:ep=RSTC_2996 on theBenchmark for (2996ds/215Mi)
% 6.16/1.67 % (2670530)First to succeed.
% 6.16/1.67 % (2670530)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2670356"
% 6.16/1.67 % (2670527)Also succeeded, but the first one will report.
% 6.16/1.67 % (2670530)Refutation found. Thanks to Tanya!
% 6.16/1.67 % SZS status Unsatisfiable for theBenchmark
% 6.16/1.67 % SZS output start Proof for theBenchmark
% See solution above
% 6.16/1.67 % (2670530)------------------------------
% 6.16/1.67 % (2670530)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.16/1.67 % (2670530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.16/1.67 % (2670530)CaDiCaL version: 2.1.3
% 6.16/1.67 % (2670530)Termination reason: Refutation
% 6.16/1.67 % (2670530)Time elapsed: 0.062 s
% 6.16/1.67 % (2670530)Peak memory usage: 89 MB
% 6.16/1.67 % (2670530)Instructions burned: 111 (million)
% 6.16/1.67 % (2670530)------------------------------
% 6.16/1.67 % (2670530)------------------------------
% 6.16/1.67 % (2670356)Success in time 0.805 s
% 6.16/1.67 % Vampire exiting
%------------------------------------------------------------------------------