%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG030-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 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 : Fri Sep 25 12:53:13 PM UTC 2026
% Result : Unsatisfiable 1.66s 6.20s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 68 ( 68 unt; 4 def)
% Number of atoms : 155 ( 67 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-4 aty)
% Number of variables : 57 ( 0 sgn 57 !; 0 ?; 36 :)
% 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(f3,axiom,
! [X0,X1] : ifeq(sorti1(X0),true,ifeq(sorti1(X1),true,sorti1(op1(X1,X0)),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
fof(f4,plain,
! [X0,X1] : true = ifeq(sorti1(X0),true,ifeq(sorti1(X1),true,sorti1(op1(X1,X0)),true),true),
inference(reorient_equations,[],[f3]) ).
fof(f7,axiom,
op1(sK2_ax3_U,sK1_ax3_V) != op1(sK1_ax3_V,sK2_ax3_U),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3_2) ).
fof(f8,axiom,
sorti1(sK1_ax3_V) = true,
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',co1_2) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq2(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f2]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] : ifeq(sorti1(X0),true,ifeq(sorti1(X1),true,sorti1(op1(X1,X0)),true),true) = true,
inference(cnf_transformation,[],[f4]) ).
tcf(c_67,plain,
op1(sK2_ax3_U,sK1_ax3_V) != op1(sK1_ax3_V,sK2_ax3_U),
inference(cnf_transformation,[],[f7]) ).
tcf(c_68,plain,
sorti1(sK1_ax3_V) = true,
inference(cnf_transformation,[],[f9]) ).
tcf(c_69,plain,
sorti1(sK2_ax3_U) = true,
inference(cnf_transformation,[],[f11]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] : ifeq2(sorti2(X0),true,ifeq2(sorti2(X1),true,op2(X1,X0),op2(X0,X1)),op2(X0,X1)) = op2(X0,X1),
inference(cnf_transformation,[],[f13]) ).
tcf(c_71,negated_conjecture,
! [X0: $i] : ifeq(sorti1(X0),true,sorti2(h(X0)),true) = true,
inference(cnf_transformation,[],[f15]) ).
tcf(c_72,negated_conjecture,
! [X0: $i,X1: $i] : 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)),
inference(cnf_transformation,[],[f17]) ).
tcf(c_73,negated_conjecture,
! [X0: $i] : ifeq2(sorti1(X0),true,j(h(X0)),X0) = X0,
inference(cnf_transformation,[],[f18]) ).
tcf(c_126,definition,
iPr_def_10 = sorti1(sK2_ax3_U),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_127,definition,
iPr_def_11 = sorti1(sK1_ax3_V),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_128,definition,
iPr_def_12 = op1(sK2_ax3_U,sK1_ax3_V),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_129,definition,
iPr_def_13 = op1(sK1_ax3_V,sK2_ax3_U),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_133,negated_conjecture,
! [X0: $i] : ifeq2(sorti1(X0),true,j(h(X0)),X0) = X0,
inference(demodulation,[status(thm)],[c_73]) ).
tcf(c_134,negated_conjecture,
! [X0: $i,X1: $i] : 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)),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_135,negated_conjecture,
! [X0: $i] : ifeq(sorti1(X0),true,sorti2(h(X0)),true) = true,
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i] : ifeq2(sorti2(X0),true,ifeq2(sorti2(X1),true,op2(X1,X0),op2(X0,X1)),op2(X0,X1)) = op2(X0,X1),
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_137,plain,
iPr_def_10 = true,
inference(demodulation,[status(thm)],[c_69,c_126]) ).
tcf(c_138,plain,
iPr_def_11 = true,
inference(demodulation,[status(thm)],[c_68,c_127]) ).
tcf(c_139,plain,
iPr_def_12 != iPr_def_13,
inference(demodulation,[status(thm)],[c_67,c_129,c_128]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i] : ifeq(sorti1(X0),true,ifeq(sorti1(X1),true,sorti1(op1(X1,X0)),true),true) = true,
inference(demodulation,[status(thm)],[c_65]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(X0,X0,X1,X2) = X1,
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq2(X0,X0,X1,X2) = X1,
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_255,plain,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_138,c_137]) ).
tcf(c_256,plain,
sorti1(sK1_ax3_V) = iPr_def_10,
inference(demodulation,[status(thm)],[c_127,c_255]) ).
tcf(c_257,plain,
! [X0: $i] : ifeq(sorti1(X0),iPr_def_10,sorti2(h(X0)),iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_135,c_137]) ).
tcf(c_258,plain,
! [X0: $i] : ifeq2(sorti1(X0),iPr_def_10,j(h(X0)),X0) = X0,
inference(demodulation,[status(thm)],[c_133,c_137]) ).
tcf(c_261,plain,
! [X0: $i,X1: $i] : ifeq(sorti1(X0),iPr_def_10,ifeq(sorti1(X1),iPr_def_10,sorti1(op1(X1,X0)),iPr_def_10),iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_141,c_137]) ).
tcf(c_263,plain,
! [X0: $i,X1: $i] : ifeq2(sorti2(X0),iPr_def_10,ifeq2(sorti2(X1),iPr_def_10,op2(X1,X0),op2(X0,X1)),op2(X0,X1)) = op2(X0,X1),
inference(demodulation,[status(thm)],[c_136,c_137]) ).
tcf(c_264,plain,
! [X0: $i,X1: $i] : ifeq2(sorti1(X0),iPr_def_10,ifeq2(sorti1(X1),iPr_def_10,op2(h(X1),h(X0)),h(op1(X1,X0))),h(op1(X1,X0))) = h(op1(X1,X0)),
inference(demodulation,[status(thm)],[c_134,c_137]) ).
tcf(c_286,plain,
ifeq(iPr_def_10,iPr_def_10,sorti2(h(sK2_ax3_U)),iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_126,c_257]) ).
tcf(c_287,plain,
ifeq(iPr_def_10,iPr_def_10,sorti2(h(sK1_ax3_V)),iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_256,c_257]) ).
tcf(c_294,plain,
ifeq(sorti1(sK1_ax3_V),iPr_def_10,ifeq(sorti1(sK2_ax3_U),iPr_def_10,sorti1(iPr_def_12),iPr_def_10),iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_128,c_261]) ).
tcf(c_295,plain,
ifeq(sorti1(sK2_ax3_U),iPr_def_10,ifeq(sorti1(sK1_ax3_V),iPr_def_10,sorti1(iPr_def_13),iPr_def_10),iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_129,c_261]) ).
tcf(c_302,plain,
ifeq2(sorti1(sK1_ax3_V),iPr_def_10,ifeq2(sorti1(sK2_ax3_U),iPr_def_10,op2(h(sK2_ax3_U),h(sK1_ax3_V)),h(iPr_def_12)),h(iPr_def_12)) = h(iPr_def_12),
inference(superposition,[status(thm)],[c_128,c_264]) ).
tcf(c_303,plain,
ifeq2(sorti1(sK2_ax3_U),iPr_def_10,ifeq2(sorti1(sK1_ax3_V),iPr_def_10,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(iPr_def_13)),h(iPr_def_13)) = h(iPr_def_13),
inference(superposition,[status(thm)],[c_129,c_264]) ).
tcf(c_353,plain,
sorti2(h(sK1_ax3_V)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_287,c_142]) ).
tcf(c_354,plain,
sorti2(h(sK2_ax3_U)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_286,c_142]) ).
tcf(c_355,plain,
sorti1(iPr_def_13) = iPr_def_10,
inference(demodulation,[status(thm)],[c_295,c_142,c_126,c_256]) ).
tcf(c_356,plain,
sorti1(iPr_def_12) = iPr_def_10,
inference(demodulation,[status(thm)],[c_294,c_142,c_126,c_256]) ).
tcf(c_361,plain,
op2(h(sK1_ax3_V),h(sK2_ax3_U)) = h(iPr_def_13),
inference(demodulation,[status(thm)],[c_303,c_143,c_126,c_256]) ).
tcf(c_362,plain,
op2(h(sK2_ax3_U),h(sK1_ax3_V)) = h(iPr_def_12),
inference(demodulation,[status(thm)],[c_302,c_143,c_126,c_256]) ).
tcf(c_374,plain,
ifeq2(iPr_def_10,iPr_def_10,j(h(iPr_def_13)),iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_355,c_258]) ).
tcf(c_380,plain,
ifeq2(iPr_def_10,iPr_def_10,j(h(iPr_def_12)),iPr_def_12) = iPr_def_12,
inference(superposition,[status(thm)],[c_356,c_258]) ).
tcf(c_415,plain,
ifeq2(sorti2(h(sK2_ax3_U)),iPr_def_10,ifeq2(sorti2(h(sK1_ax3_V)),iPr_def_10,op2(h(sK1_ax3_V),h(sK2_ax3_U)),h(iPr_def_12)),h(iPr_def_12)) = h(iPr_def_12),
inference(superposition,[status(thm)],[c_362,c_263]) ).
tcf(c_505,plain,
j(h(iPr_def_12)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_380,c_143]) ).
tcf(c_507,plain,
j(h(iPr_def_13)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_374,c_143]) ).
tcf(c_538,plain,
h(iPr_def_12) = h(iPr_def_13),
inference(demodulation,[status(thm)],[c_415,c_143,c_353,c_354,c_361]) ).
tcf(c_751,plain,
j(h(iPr_def_13)) = iPr_def_12,
inference(superposition,[status(thm)],[c_538,c_505]) ).
tcf(c_959,plain,
iPr_def_12 = iPr_def_13,
inference(demodulation,[status(thm)],[c_751,c_507]) ).
tcf(c_960,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_959,c_139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG030-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/5.38 % Computer : n001.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Fri Sep 25 04:39:01 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/5.42 Running UEQ theorem proving
% 0.16/5.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.43
% 0.16/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.43
% 0.16/5.43 % Detected problem language: tptp
% 0.16/5.45 % Proving...
% 1.66/6.20 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 1.66/6.20 % SZS status Started for theBenchmark.p
% 1.66/6.20 % SZS status Unsatisfiable for theBenchmark.p
% 1.66/6.20
% 1.66/6.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.66/6.20
% 1.66/6.20 % ------ iProver source info
% 1.66/6.20
% 1.66/6.20 % git: date: 2026-07-19 20:42:38 +0200
% 1.66/6.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.66/6.20 % git: non_committed_changes: false
% 1.66/6.20
% 1.66/6.20 % ------ Parsing...% successful
% 1.66/6.20
% 1.66/6.20
% 1.66/6.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.66/6.20
% 1.66/6.20 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.66/6.20
% 1.66/6.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.66/6.20
% 1.66/6.20 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.66/6.20 % ------ Proving...
% 1.66/6.20 % ------ Problem Properties
% 1.66/6.20
% 1.66/6.20 %
% 1.66/6.20 % clauses 18
% 1.66/6.20 % conjectures 6
% 1.66/6.20 % EPR 3
% 1.66/6.20 % Horn 18
% 1.66/6.20 % unary 18
% 1.66/6.20 % binary 0
% 1.66/6.20 % lits 18
% 1.66/6.20 % lits eq 18
% 1.66/6.20 % fd_pure 0
% 1.66/6.20 % fd_pseudo 0
% 1.66/6.20 % fd_cond 0
% 1.66/6.20 % fd_pseudo_cond 0
% 1.66/6.20 % AC symbols 0
% 1.66/6.20
% 1.66/6.20 % ------ Input Options Time Limit: Unbounded
% 1.66/6.20
% 1.66/6.20
% 1.66/6.20 % ------
% 1.66/6.20 % Current options:
% 1.66/6.20 % ------
% 1.66/6.20
% 1.66/6.20
% 1.66/6.20 %
% 1.66/6.20
% 1.66/6.20 % ------ Proving...
% 1.66/6.20 %
% 1.66/6.20
% 1.66/6.20 % SZS status Unsatisfiable for theBenchmark.p
% 1.66/6.20
% 1.66/6.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.66/6.20
% 1.66/6.20
%------------------------------------------------------------------------------