%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG030-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 09:20:09 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.25s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 55 unt; 0 def)
% Number of atoms : 55 ( 54 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 1 ( 1 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-4 aty)
% Number of variables : 25 ( 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
fof(f7,axiom,
op1(sK2_ax3_U,sK1_ax3_V) != op1(sK1_ax3_V,sK2_ax3_U),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3_2) ).
fof(f8,axiom,
sorti1(sK1_ax3_V) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3_1) ).
fof(f9,plain,
true = sorti1(sK1_ax3_V),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
sorti1(sK2_ax3_U) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f11,plain,
true = sorti1(sK2_ax3_U),
inference(reorient_equations,[],[f10]) ).
fof(f12,axiom,
! [X0,X1] : ifeq2(sorti2(X0),true,ifeq2(sorti2(X1),true,op2(X1,X0),op2(X0,X1)),op2(X0,X1)) = op2(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f13,plain,
! [X0,X1] : op2(X0,X1) = ifeq2(sorti2(X0),true,ifeq2(sorti2(X1),true,op2(X1,X0),op2(X0,X1)),op2(X0,X1)),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
! [X0] : ifeq(sorti1(X0),true,sorti2(h(X0)),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f15,plain,
! [X0] : true = ifeq(sorti1(X0),true,sorti2(h(X0)),true),
inference(reorient_equations,[],[f14]) ).
fof(f16,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/sandbox2/benchmark/theBenchmark.p',co1_1) ).
fof(f17,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,[],[f16]) ).
fof(f18,negated_conjecture,
! [X0] : ifeq2(sorti1(X0),true,j(h(X0)),X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_2) ).
fof(f21,negated_conjecture,
! [X0,X1] : ifeq2(sorti2(X0),true,ifeq2(sorti2(X1),true,op1(j(X1),j(X0)),j(op2(X1,X0))),j(op2(X1,X0))) = j(op2(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
fof(f22,plain,
! [X0,X1] : j(op2(X1,X0)) = ifeq2(sorti2(X0),true,ifeq2(sorti2(X1),true,op1(j(X1),j(X0)),j(op2(X1,X0))),j(op2(X1,X0))),
inference(reorient_equations,[],[f21]) ).
fof(f24,plain,
! [X0] : h(op1(sK1_ax3_V,X0)) = ifeq2(sorti1(X0),true,ifeq2(true,true,op2(h(sK1_ax3_V),h(X0)),h(op1(sK1_ax3_V,X0))),h(op1(sK1_ax3_V,X0))),
inference(superposition,[],[f17,f9]) ).
fof(f25,plain,
! [X0] : h(op1(X0,sK1_ax3_V)) = ifeq2(true,true,ifeq2(sorti1(X0),true,op2(h(X0),h(sK1_ax3_V)),h(op1(X0,sK1_ax3_V))),h(op1(X0,sK1_ax3_V))),
inference(superposition,[],[f17,f9]) ).
fof(f26,plain,
sK1_ax3_V = ifeq2(true,true,j(h(sK1_ax3_V)),sK1_ax3_V),
inference(superposition,[],[f18,f9]) ).
fof(f27,plain,
true = ifeq(true,true,sorti2(h(sK1_ax3_V)),true),
inference(superposition,[],[f15,f9]) ).
fof(f30,plain,
sK2_ax3_U = ifeq2(true,true,j(h(sK2_ax3_U)),sK2_ax3_U),
inference(superposition,[],[f18,f11]) ).
fof(f31,plain,
true = ifeq(true,true,sorti2(h(sK2_ax3_U)),true),
inference(superposition,[],[f15,f11]) ).
fof(f32,plain,
sK1_ax3_V = j(h(sK1_ax3_V)),
inference(superposition,[],[f1,f26]) ).
fof(f42,plain,
true = sorti2(h(sK1_ax3_V)),
inference(forward_demodulation,[],[f27,f2]) ).
fof(f68,plain,
sK2_ax3_U = j(h(sK2_ax3_U)),
inference(forward_demodulation,[],[f30,f1]) ).
fof(f80,plain,
true = sorti2(h(sK2_ax3_U)),
inference(forward_demodulation,[],[f31,f2]) ).
fof(f102,plain,
! [X0] : h(op1(sK1_ax3_V,X0)) = ifeq2(sorti1(X0),true,op2(h(sK1_ax3_V),h(X0)),h(op1(sK1_ax3_V,X0))),
inference(forward_demodulation,[],[f24,f1]) ).
fof(f105,plain,
h(op1(sK1_ax3_V,sK2_ax3_U)) = ifeq2(true,true,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(op1(sK1_ax3_V,sK2_ax3_U))),
inference(superposition,[],[f102,f11]) ).
fof(f108,plain,
h(op1(sK1_ax3_V,sK2_ax3_U)) = op2(h(sK1_ax3_V),h(sK2_ax3_U)),
inference(forward_demodulation,[],[f105,f1]) ).
fof(f111,plain,
! [X0] : h(op1(X0,sK1_ax3_V)) = ifeq2(sorti1(X0),true,op2(h(X0),h(sK1_ax3_V)),h(op1(X0,sK1_ax3_V))),
inference(forward_demodulation,[],[f25,f1]) ).
fof(f117,plain,
j(h(op1(sK1_ax3_V,sK2_ax3_U))) = ifeq2(sorti2(h(sK2_ax3_U)),true,ifeq2(sorti2(h(sK1_ax3_V)),true,op1(j(h(sK1_ax3_V)),j(h(sK2_ax3_U))),j(h(op1(sK1_ax3_V,sK2_ax3_U)))),j(h(op1(sK1_ax3_V,sK2_ax3_U)))),
inference(superposition,[],[f22,f108]) ).
fof(f118,plain,
j(h(op1(sK1_ax3_V,sK2_ax3_U))) = ifeq2(sorti2(h(sK2_ax3_U)),true,ifeq2(sorti2(h(sK1_ax3_V)),true,op1(j(h(sK1_ax3_V)),sK2_ax3_U),j(h(op1(sK1_ax3_V,sK2_ax3_U)))),j(h(op1(sK1_ax3_V,sK2_ax3_U)))),
inference(forward_demodulation,[],[f117,f68]) ).
fof(f124,plain,
j(h(op1(sK1_ax3_V,sK2_ax3_U))) = ifeq2(sorti2(h(sK2_ax3_U)),true,ifeq2(sorti2(h(sK1_ax3_V)),true,op1(sK1_ax3_V,sK2_ax3_U),j(h(op1(sK1_ax3_V,sK2_ax3_U)))),j(h(op1(sK1_ax3_V,sK2_ax3_U)))),
inference(forward_demodulation,[],[f118,f32]) ).
fof(f129,plain,
j(h(op1(sK1_ax3_V,sK2_ax3_U))) = ifeq2(sorti2(h(sK2_ax3_U)),true,ifeq2(true,true,op1(sK1_ax3_V,sK2_ax3_U),j(h(op1(sK1_ax3_V,sK2_ax3_U)))),j(h(op1(sK1_ax3_V,sK2_ax3_U)))),
inference(forward_demodulation,[],[f124,f42]) ).
fof(f134,plain,
j(h(op1(sK1_ax3_V,sK2_ax3_U))) = ifeq2(sorti2(h(sK2_ax3_U)),true,op1(sK1_ax3_V,sK2_ax3_U),j(h(op1(sK1_ax3_V,sK2_ax3_U)))),
inference(forward_demodulation,[],[f129,f1]) ).
fof(f138,plain,
j(h(op1(sK1_ax3_V,sK2_ax3_U))) = ifeq2(true,true,op1(sK1_ax3_V,sK2_ax3_U),j(h(op1(sK1_ax3_V,sK2_ax3_U)))),
inference(forward_demodulation,[],[f134,f80]) ).
fof(f139,plain,
op1(sK1_ax3_V,sK2_ax3_U) = j(h(op1(sK1_ax3_V,sK2_ax3_U))),
inference(forward_demodulation,[],[f138,f1]) ).
fof(f141,plain,
h(op1(sK2_ax3_U,sK1_ax3_V)) = ifeq2(true,true,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(op1(sK2_ax3_U,sK1_ax3_V))),
inference(superposition,[],[f111,f11]) ).
fof(f144,plain,
op2(h(sK2_ax3_U),h(sK1_ax3_V)) = h(op1(sK2_ax3_U,sK1_ax3_V)),
inference(forward_demodulation,[],[f141,f1]) ).
fof(f398,plain,
op2(h(sK1_ax3_V),h(sK2_ax3_U)) = ifeq2(sorti2(h(sK1_ax3_V)),true,ifeq2(sorti2(h(sK2_ax3_U)),true,h(op1(sK2_ax3_U,sK1_ax3_V)),op2(h(sK1_ax3_V),h(sK2_ax3_U))),op2(h(sK1_ax3_V),h(sK2_ax3_U))),
inference(superposition,[],[f13,f144]) ).
fof(f400,plain,
j(h(op1(sK2_ax3_U,sK1_ax3_V))) = ifeq2(sorti2(h(sK1_ax3_V)),true,ifeq2(sorti2(h(sK2_ax3_U)),true,op1(j(h(sK2_ax3_U)),j(h(sK1_ax3_V))),j(h(op1(sK2_ax3_U,sK1_ax3_V)))),j(h(op1(sK2_ax3_U,sK1_ax3_V)))),
inference(superposition,[],[f22,f144]) ).
fof(f401,plain,
j(h(op1(sK2_ax3_U,sK1_ax3_V))) = ifeq2(sorti2(h(sK1_ax3_V)),true,ifeq2(sorti2(h(sK2_ax3_U)),true,op1(j(h(sK2_ax3_U)),sK1_ax3_V),j(h(op1(sK2_ax3_U,sK1_ax3_V)))),j(h(op1(sK2_ax3_U,sK1_ax3_V)))),
inference(forward_demodulation,[],[f400,f32]) ).
fof(f403,plain,
h(op1(sK1_ax3_V,sK2_ax3_U)) = ifeq2(sorti2(h(sK1_ax3_V)),true,ifeq2(sorti2(h(sK2_ax3_U)),true,h(op1(sK2_ax3_U,sK1_ax3_V)),h(op1(sK1_ax3_V,sK2_ax3_U))),h(op1(sK1_ax3_V,sK2_ax3_U))),
inference(forward_demodulation,[],[f398,f108]) ).
fof(f408,plain,
j(h(op1(sK2_ax3_U,sK1_ax3_V))) = ifeq2(sorti2(h(sK1_ax3_V)),true,ifeq2(sorti2(h(sK2_ax3_U)),true,op1(sK2_ax3_U,sK1_ax3_V),j(h(op1(sK2_ax3_U,sK1_ax3_V)))),j(h(op1(sK2_ax3_U,sK1_ax3_V)))),
inference(forward_demodulation,[],[f401,f68]) ).
fof(f410,plain,
h(op1(sK1_ax3_V,sK2_ax3_U)) = ifeq2(sorti2(h(sK1_ax3_V)),true,ifeq2(true,true,h(op1(sK2_ax3_U,sK1_ax3_V)),h(op1(sK1_ax3_V,sK2_ax3_U))),h(op1(sK1_ax3_V,sK2_ax3_U))),
inference(forward_demodulation,[],[f403,f80]) ).
fof(f413,plain,
j(h(op1(sK2_ax3_U,sK1_ax3_V))) = ifeq2(sorti2(h(sK1_ax3_V)),true,ifeq2(true,true,op1(sK2_ax3_U,sK1_ax3_V),j(h(op1(sK2_ax3_U,sK1_ax3_V)))),j(h(op1(sK2_ax3_U,sK1_ax3_V)))),
inference(forward_demodulation,[],[f408,f80]) ).
fof(f415,plain,
h(op1(sK1_ax3_V,sK2_ax3_U)) = ifeq2(sorti2(h(sK1_ax3_V)),true,h(op1(sK2_ax3_U,sK1_ax3_V)),h(op1(sK1_ax3_V,sK2_ax3_U))),
inference(forward_demodulation,[],[f410,f1]) ).
fof(f418,plain,
j(h(op1(sK2_ax3_U,sK1_ax3_V))) = ifeq2(sorti2(h(sK1_ax3_V)),true,op1(sK2_ax3_U,sK1_ax3_V),j(h(op1(sK2_ax3_U,sK1_ax3_V)))),
inference(forward_demodulation,[],[f413,f1]) ).
fof(f420,plain,
h(op1(sK1_ax3_V,sK2_ax3_U)) = ifeq2(true,true,h(op1(sK2_ax3_U,sK1_ax3_V)),h(op1(sK1_ax3_V,sK2_ax3_U))),
inference(forward_demodulation,[],[f415,f42]) ).
fof(f422,plain,
j(h(op1(sK2_ax3_U,sK1_ax3_V))) = ifeq2(true,true,op1(sK2_ax3_U,sK1_ax3_V),j(h(op1(sK2_ax3_U,sK1_ax3_V)))),
inference(forward_demodulation,[],[f418,f42]) ).
fof(f423,plain,
h(op1(sK1_ax3_V,sK2_ax3_U)) = h(op1(sK2_ax3_U,sK1_ax3_V)),
inference(forward_demodulation,[],[f420,f1]) ).
fof(f425,plain,
op1(sK2_ax3_U,sK1_ax3_V) = j(h(op1(sK2_ax3_U,sK1_ax3_V))),
inference(forward_demodulation,[],[f422,f1]) ).
fof(f1135,plain,
op1(sK1_ax3_V,sK2_ax3_U) = j(h(op1(sK2_ax3_U,sK1_ax3_V))),
inference(superposition,[],[f139,f423]) ).
fof(f1479,plain,
op1(sK2_ax3_U,sK1_ax3_V) = op1(sK1_ax3_V,sK2_ax3_U),
inference(forward_demodulation,[],[f1135,f425]) ).
fof(f1480,plain,
$false,
inference(forward_subsumption_resolution,[],[f1479,f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG030-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.16 % Computer : n018.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Mon Sep 28 19:21:55 UTC 2026
% 0.10/0.16 % CPUTime :
% 0.10/0.16 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 Running first-order model finding
% 0.10/0.19 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.25 % (3686812)Will run a generic schedule for satisfiability detection.
% 0.10/0.25 % (3686820)dis+10_1_sil=32000:sp=arity:random_seed=1664046927:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.25 % (3686818)% WARNING: option uhcvi not known.
% 0.10/0.25 % (3686817)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=290626207_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.25 % (3686819)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3793910626:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.25 % (3686821)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3075725548:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.25 % (3686822)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2667905258:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.25 % (3686823)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2678303145:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.25 % (3686818)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=928119562:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.25 % TRYING [1]
% 0.10/0.25 % TRYING [2]
% 0.10/0.25 % TRYING [3]
% 0.10/0.25 % (3686820) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3686812-3686820"...
% 0.10/0.25 % (3686820)...printing done.
% 0.10/0.25 % (3686820)Refutation found. Thanks to Tanya!
% 0.10/0.25 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.25 % (3686820)------------------------------
% 0.10/0.25 % (3686820)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.25 % (3686820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.25 % (3686820)CaDiCaL version: 2.1.3
% 0.10/0.25 % (3686820)Termination reason: Refutation
% 0.10/0.25 % (3686820)Time elapsed: 0.016 s
% 0.10/0.25 % (3686820)Peak memory usage: 11 MB
% 0.10/0.25 % (3686820)Instructions burned: 58 (million)
% 0.10/0.25 % (3686812)Success in time 0.053 s
% 0.10/0.25 % Vampire exiting
%------------------------------------------------------------------------------