%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n020.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 09:09:29 AM UTC 2026
% Result : Unsatisfiable 2.70s 1.15s
% Output : Refutation 2.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 40 ( 40 unt; 1 def)
% Number of atoms : 40 ( 34 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-4 aty)
% Number of variables : 27 ( 27 !; 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(f23,definition,
~ sP0(tuple(sK1_ax4_U,true)),
introduced(definition,[new_symbols(definition,[sP0])],[inequality_splitting_name_introduction]) ).
fof(f24,plain,
! [X0] : sP0(tuple(op2(X0,X0),sorti2(X0))),
inference(inequality_splitting,[],[f10,f23]) ).
fof(f25,plain,
! [X0] : sorti2(sK1_ax4_U) = ifeq(sorti1(X0),sorti2(sK1_ax4_U),sorti2(h(X0)),sorti2(sK1_ax4_U)),
inference(backward_demodulation,[],[f14,f12]) ).
fof(f26,plain,
! [X0,X1] : h(op1(X1,X0)) = ifeq2(sorti1(X0),sorti2(sK1_ax4_U),ifeq2(sorti1(X1),sorti2(sK1_ax4_U),op2(h(X1),h(X0)),h(op1(X1,X0))),h(op1(X1,X0))),
inference(backward_demodulation,[],[f16,f12]) ).
fof(f28,plain,
! [X0] : sorti2(sK1_ax4_U) = ifeq(sorti2(X0),sorti2(sK1_ax4_U),sorti1(j(X0)),sorti2(sK1_ax4_U)),
inference(backward_demodulation,[],[f19,f12]) ).
fof(f30,plain,
! [X0] : ifeq2(sorti2(X0),sorti2(sK1_ax4_U),h(j(X0)),X0) = X0,
inference(backward_demodulation,[],[f22,f12]) ).
fof(f31,plain,
~ sP0(tuple(sK1_ax4_U,sorti2(sK1_ax4_U))),
inference(backward_demodulation,[],[f23,f12]) ).
fof(f32,plain,
! [X0] : ifeq2(sorti1(X0),sorti2(sK1_ax4_U),op1(sK2_ax3_V(X0),sK2_ax3_V(X0)),X0) = X0,
inference(forward_demodulation,[],[f9,f12]) ).
fof(f33,plain,
! [X0] : sorti2(sK1_ax4_U) = ifeq(sorti1(X0),sorti2(sK1_ax4_U),sorti1(sK2_ax3_V(X0)),sorti2(sK1_ax4_U)),
inference(forward_demodulation,[],[f8,f12]) ).
fof(f38,plain,
sK1_ax4_U = h(j(sK1_ax4_U)),
inference(superposition,[],[f30,f1]) ).
fof(f42,plain,
sorti2(sK1_ax4_U) = sorti1(j(sK1_ax4_U)),
inference(superposition,[],[f28,f2]) ).
fof(f65,plain,
j(sK1_ax4_U) = ifeq2(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))),j(sK1_ax4_U)),
inference(superposition,[],[f32,f42]) ).
fof(f66,plain,
j(sK1_ax4_U) = op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))),
inference(forward_demodulation,[],[f65,f1]) ).
fof(f68,plain,
h(j(sK1_ax4_U)) = ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U),ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U),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,[],[f26,f66]) ).
fof(f69,plain,
sK1_ax4_U = ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U),ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U),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,[],[f68,f38]) ).
fof(f71,plain,
sorti2(sK1_ax4_U) = ifeq(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),sorti1(sK2_ax3_V(j(sK1_ax4_U))),sorti2(sK1_ax4_U)),
inference(superposition,[],[f33,f42]) ).
fof(f72,plain,
sorti2(sK1_ax4_U) = sorti1(sK2_ax3_V(j(sK1_ax4_U))),
inference(forward_demodulation,[],[f71,f2]) ).
fof(f73,plain,
sK1_ax4_U = ifeq2(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),ifeq2(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),sK1_ax4_U),sK1_ax4_U),
inference(backward_demodulation,[],[f69,f72]) ).
fof(f74,plain,
sK1_ax4_U = ifeq2(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),sK1_ax4_U),
inference(forward_demodulation,[],[f73,f1]) ).
fof(f75,plain,
sK1_ax4_U = op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),
inference(forward_demodulation,[],[f74,f1]) ).
fof(f81,plain,
sorti2(sK1_ax4_U) = ifeq(sorti2(sK1_ax4_U),sorti2(sK1_ax4_U),sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),sorti2(sK1_ax4_U)),
inference(superposition,[],[f25,f72]) ).
fof(f84,plain,
sorti2(sK1_ax4_U) = sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),
inference(forward_demodulation,[],[f81,f2]) ).
fof(f94,plain,
sP0(tuple(op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))),sorti2(sK1_ax4_U))),
inference(superposition,[],[f24,f84]) ).
fof(f107,plain,
sP0(tuple(sK1_ax4_U,sorti2(sK1_ax4_U))),
inference(forward_demodulation,[],[f94,f75]) ).
fof(f112,plain,
$false,
inference(forward_subsumption_resolution,[],[f107,f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG069-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n020.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 19:25:20 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 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
% 2.70/1.15 % (449157)Detected a unit-equality problem, will run specialized UEQ schedule.
% 2.70/1.15 % (449165)ott-1010_1_sfv=off:to=lpo:sil=8000:fdtod=off:sp=reverse_frequency:spb=goal_then_units:fd=preordered:random_seed=4120006875:i=136:bd=preordered:ins=2:av=off_2999 on theBenchmark for (2999ds/136Mi)
% 2.70/1.15 % (449165)First to succeed.
% 2.70/1.15 % (449165)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-449157"
% 2.70/1.15 % (449162)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=2512654782:i=138329:kws=inv_arity_squared:fgj=on:bd=preordered_2999 on theBenchmark for (2999ds/138329Mi)
% 2.70/1.15 % (449168)dis-1010_7_sil=8000:fde=unused:flr=on:random_seed=2889896006:i=1187:sd=4:av=off:ss=axioms:sgt=32_2999 on theBenchmark for (2999ds/1187Mi)
% 2.70/1.15 % (449164)lrs+10_1_ncem=casc2026/models/loop5.pt:sil=128000:tgt=ground:npcc=on:spb=goal_then_units:urr=ec_only:random_seed=2281524838:i=130716:gtgl=4:add=on:doe=on:bd=all:gtg=exists_sym_2999 on theBenchmark for (2999ds/130716Mi)
% 2.70/1.15 % (449163)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=2838521983:i=130792:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/130792Mi)
% 2.70/1.15 % (449167)lrs+10_3_to=lpo:sil=64000:drc=off:fde=unused:sp=reverse_frequency:acc=on:bsr=on:fd=preordered:nwc=1:random_seed=2716422907:avsq=on:i=257:avsqr=16,3:bd=preordered:fsr=off_2999 on theBenchmark for (2999ds/257Mi)
% 2.70/1.15 % (449166)dis+10_14_to=lpo:sil=8000:tgt=full:drc=off:sp=const_frequency:sos=all:random_seed=3613652050:i=181:gtgl=5:bs=unit_only:fsr=off:gtg=exists_all_2999 on theBenchmark for (2999ds/181Mi)
% 2.70/1.15 % (449168)Also succeeded, but the first one will report.
% 2.70/1.15 % (449167)Also succeeded, but the first one will report.
% 2.70/1.15 % (449166)Also succeeded, but the first one will report.
% 2.70/1.15 % (449165)Refutation found. Thanks to Tanya!
% 2.70/1.15 % SZS status Unsatisfiable for theBenchmark
% 2.70/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.70/1.15 % (449165)------------------------------
% 2.70/1.15 % (449165)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.15 % (449165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.15 % (449165)CaDiCaL version: 2.1.3
% 2.70/1.15 % (449165)Termination reason: Refutation
% 2.70/1.15 % (449165)Time elapsed: 0.003 s
% 2.70/1.15 % (449165)Peak memory usage: 88 MB
% 2.70/1.15 % (449165)Instructions burned: 7 (million)
% 2.70/1.15 % (449165)------------------------------
% 2.70/1.15 % (449165)------------------------------
% 2.70/1.15 % (449157)Success in time 0.289 s
% 2.70/1.15 % Vampire exiting
%------------------------------------------------------------------------------