%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG069-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 09:21:13 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.26s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 33 unt; 0 def)
% Number of atoms : 33 ( 32 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-4 aty)
% Number of variables : 19 ( 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
fof(f7,axiom,
! [X0] : ifeq(sorti1(X0),true,sorti1(sK2_ax3_V(X0)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3_1) ).
fof(f8,plain,
! [X0] : true = ifeq(sorti1(X0),true,sorti1(sK2_ax3_V(X0)),true),
inference(reorient_equations,[],[f7]) ).
fof(f9,axiom,
! [X0] : ifeq2(sorti1(X0),true,op1(sK2_ax3_V(X0),sK2_ax3_V(X0)),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f10,axiom,
! [X0] : tuple(op2(X0,X0),sorti2(X0)) != tuple(sK1_ax4_U,true),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4_1) ).
fof(f11,axiom,
sorti2(sK1_ax4_U) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f12,plain,
true = sorti2(sK1_ax4_U),
inference(reorient_equations,[],[f11]) ).
fof(f13,negated_conjecture,
! [X0] : ifeq(sorti1(X0),true,sorti2(h(X0)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f14,plain,
! [X0] : true = ifeq(sorti1(X0),true,sorti2(h(X0)),true),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
! [X0,X1] : ifeq2(sorti1(X0),true,ifeq2(sorti1(X1),true,op2(h(X1),h(X0)),h(op1(X1,X0))),h(op1(X1,X0))) = h(op1(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
fof(f16,plain,
! [X0,X1] : h(op1(X1,X0)) = ifeq2(sorti1(X0),true,ifeq2(sorti1(X1),true,op2(h(X1),h(X0)),h(op1(X1,X0))),h(op1(X1,X0))),
inference(reorient_equations,[],[f15]) ).
fof(f18,negated_conjecture,
! [X0] : ifeq(sorti2(X0),true,sorti1(j(X0)),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
fof(f19,plain,
! [X0] : true = ifeq(sorti2(X0),true,sorti1(j(X0)),true),
inference(reorient_equations,[],[f18]) ).
fof(f22,negated_conjecture,
! [X0] : ifeq2(sorti2(X0),true,h(j(X0)),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f25,plain,
sK1_ax4_U = ifeq2(true,true,h(j(sK1_ax4_U)),sK1_ax4_U),
inference(superposition,[],[f22,f12]) ).
fof(f26,plain,
true = ifeq(true,true,sorti1(j(sK1_ax4_U)),true),
inference(superposition,[],[f19,f12]) ).
fof(f28,plain,
sK1_ax4_U = h(j(sK1_ax4_U)),
inference(superposition,[],[f1,f25]) ).
fof(f31,plain,
true = sorti1(j(sK1_ax4_U)),
inference(superposition,[],[f2,f26]) ).
fof(f43,plain,
true = ifeq(true,true,sorti1(sK2_ax3_V(j(sK1_ax4_U))),true),
inference(superposition,[],[f8,f31]) ).
fof(f56,plain,
j(sK1_ax4_U) = ifeq2(true,true,op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))),j(sK1_ax4_U)),
inference(superposition,[],[f9,f31]) ).
fof(f88,plain,
true = sorti1(sK2_ax3_V(j(sK1_ax4_U))),
inference(superposition,[],[f43,f2]) ).
fof(f125,plain,
true = ifeq(true,true,sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),true),
inference(superposition,[],[f14,f88]) ).
fof(f165,plain,
j(sK1_ax4_U) = op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))),
inference(superposition,[],[f56,f1]) ).
fof(f184,plain,
h(j(sK1_ax4_U)) = ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),h(j(sK1_ax4_U))),h(j(sK1_ax4_U))),
inference(superposition,[],[f16,f165]) ).
fof(f185,plain,
sK1_ax4_U = ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),true,op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),sK1_ax4_U),sK1_ax4_U),
inference(forward_demodulation,[],[f184,f28]) ).
fof(f188,plain,
sK1_ax4_U = ifeq2(true,true,ifeq2(true,true,op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),sK1_ax4_U),sK1_ax4_U),
inference(forward_demodulation,[],[f185,f88]) ).
fof(f190,plain,
sK1_ax4_U = ifeq2(true,true,op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),sK1_ax4_U),
inference(forward_demodulation,[],[f188,f1]) ).
fof(f342,plain,
true = sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),
inference(superposition,[],[f125,f2]) ).
fof(f745,plain,
sK1_ax4_U = op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),
inference(superposition,[],[f190,f1]) ).
fof(f877,plain,
tuple(sK1_ax4_U,true) != tuple(sK1_ax4_U,sorti2(h(sK2_ax3_V(j(sK1_ax4_U))))),
inference(superposition,[],[f10,f745]) ).
fof(f882,plain,
tuple(sK1_ax4_U,true) != tuple(sK1_ax4_U,true),
inference(forward_demodulation,[],[f877,f342]) ).
fof(f883,plain,
$false,
inference(trivial_inequality_removal,[],[f882]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG069-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n001.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 19:30:19 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.26 % (651261)Will run a generic schedule for satisfiability detection.
% 0.18/0.26 % (651267)% WARNING: option uhcvi not known.
% 0.18/0.26 % (651267)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4274397159:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.26 % (651266)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2851960007_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.26 % (651271)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=811470277:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.26 % (651268)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1171903990:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.26 % (651269)dis+10_1_sil=32000:sp=arity:random_seed=265958516:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.26 % (651270)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1790962944:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.26 % (651272)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1036037501:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.26 % TRYING [1]
% 0.18/0.26 % TRYING [2]
% 0.18/0.26 % TRYING [3]
% 0.18/0.26 % (651267) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-651261-651267"...
% 0.18/0.26 % (651267)...printing done.
% 0.18/0.26 % (651267)Refutation found. Thanks to Tanya!
% 0.18/0.26 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.27 % (651267)------------------------------
% 0.18/0.27 % (651267)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.27 % (651267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.27 % (651267)CaDiCaL version: 2.1.3
% 0.18/0.27 % (651267)Termination reason: Refutation
% 0.18/0.27 % (651267)Time elapsed: 0.014 s
% 0.18/0.27 % (651267)Peak memory usage: 11 MB
% 0.18/0.27 % (651267)Instructions burned: 45 (million)
% 0.18/0.27 % (651261)Success in time 0.042 s
% 0.18/0.27 % Vampire exiting
%------------------------------------------------------------------------------