%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG069-10 : 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 : n002.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 12:53:20 PM UTC 2026
% Result : Unsatisfiable 1.77s 6.29s
% Output : CNFRefutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 12
% Syntax : Number of formulae : 58 ( 58 unt; 2 def)
% Number of atoms : 99 ( 57 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 2 con; 0-4 aty)
% Number of variables : 54 ( 0 sgn 54 !; 0 ?; 35 :)
% 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) ).
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_67,plain,
! [X0: $i] : ifeq(sorti1(X0),true,sorti1(sK2_ax3_V(X0)),true) = true,
inference(cnf_transformation,[],[f8]) ).
tcf(c_68,plain,
! [X0: $i] : ifeq2(sorti1(X0),true,op1(sK2_ax3_V(X0),sK2_ax3_V(X0)),X0) = X0,
inference(cnf_transformation,[],[f9]) ).
tcf(c_69,plain,
! [X0: $i] : tuple(op2(X0,X0),sorti2(X0)) != tuple(sK1_ax4_U,true),
inference(cnf_transformation,[],[f10]) ).
tcf(c_70,plain,
sorti2(sK1_ax4_U) = true,
inference(cnf_transformation,[],[f12]) ).
tcf(c_71,negated_conjecture,
! [X0: $i] : ifeq(sorti1(X0),true,sorti2(h(X0)),true) = true,
inference(cnf_transformation,[],[f14]) ).
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,[],[f16]) ).
tcf(c_74,negated_conjecture,
! [X0: $i] : ifeq(sorti2(X0),true,sorti1(j(X0)),true) = true,
inference(cnf_transformation,[],[f19]) ).
tcf(c_76,negated_conjecture,
! [X0: $i] : ifeq2(sorti2(X0),true,h(j(X0)),X0) = X0,
inference(cnf_transformation,[],[f22]) ).
tcf(c_129,definition,
iPr_def_10 = sorti2(sK1_ax4_U),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_130,definition,
iPr_def_11 = tuple(sK1_ax4_U,true),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_131,negated_conjecture,
! [X0: $i] : ifeq2(sorti2(X0),true,h(j(X0)),X0) = X0,
inference(demodulation,[status(thm)],[c_76]) ).
tcf(c_133,negated_conjecture,
! [X0: $i] : ifeq(sorti2(X0),true,sorti1(j(X0)),true) = true,
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_135,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_136,negated_conjecture,
! [X0: $i] : ifeq(sorti1(X0),true,sorti2(h(X0)),true) = true,
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_137,plain,
iPr_def_10 = true,
inference(demodulation,[status(thm)],[c_70,c_129]) ).
tcf(c_138,plain,
! [X0: $i] : tuple(op2(X0,X0),sorti2(X0)) != iPr_def_11,
inference(demodulation,[status(thm)],[c_69,c_130]) ).
tcf(c_139,plain,
! [X0: $i] : ifeq2(sorti1(X0),true,op1(sK2_ax3_V(X0),sK2_ax3_V(X0)),X0) = X0,
inference(demodulation,[status(thm)],[c_68]) ).
tcf(c_140,plain,
! [X0: $i] : ifeq(sorti1(X0),true,sorti1(sK2_ax3_V(X0)),true) = true,
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(X0,X0,X1,X2) = X1,
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq2(X0,X0,X1,X2) = X1,
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_261,plain,
tuple(sK1_ax4_U,iPr_def_10) = iPr_def_11,
inference(demodulation,[status(thm)],[c_130,c_137]) ).
tcf(c_262,plain,
! [X0: $i] : ifeq(sorti1(X0),iPr_def_10,sorti1(sK2_ax3_V(X0)),iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_140,c_137]) ).
tcf(c_263,plain,
! [X0: $i] : ifeq(sorti1(X0),iPr_def_10,sorti2(h(X0)),iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_136,c_137]) ).
tcf(c_265,plain,
! [X0: $i] : ifeq(sorti2(X0),iPr_def_10,sorti1(j(X0)),iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_133,c_137]) ).
tcf(c_266,plain,
! [X0: $i] : ifeq2(sorti2(X0),iPr_def_10,h(j(X0)),X0) = X0,
inference(demodulation,[status(thm)],[c_131,c_137]) ).
tcf(c_267,plain,
! [X0: $i] : ifeq2(sorti1(X0),iPr_def_10,op1(sK2_ax3_V(X0),sK2_ax3_V(X0)),X0) = X0,
inference(demodulation,[status(thm)],[c_139,c_137]) ).
tcf(c_270,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_135,c_137]) ).
tcf(c_294,plain,
ifeq(iPr_def_10,iPr_def_10,sorti1(j(sK1_ax4_U)),iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_129,c_265]) ).
tcf(c_295,plain,
ifeq2(iPr_def_10,iPr_def_10,h(j(sK1_ax4_U)),sK1_ax4_U) = sK1_ax4_U,
inference(superposition,[status(thm)],[c_129,c_266]) ).
tcf(c_300,plain,
h(j(sK1_ax4_U)) = sK1_ax4_U,
inference(demodulation,[status(thm)],[c_295,c_144]) ).
tcf(c_301,plain,
sorti1(j(sK1_ax4_U)) = iPr_def_10,
inference(demodulation,[status(thm)],[c_294,c_143]) ).
tcf(c_324,plain,
ifeq2(iPr_def_10,iPr_def_10,op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))),j(sK1_ax4_U)) = j(sK1_ax4_U),
inference(superposition,[status(thm)],[c_301,c_267]) ).
tcf(c_326,plain,
ifeq(iPr_def_10,iPr_def_10,sorti1(sK2_ax3_V(j(sK1_ax4_U))),iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_301,c_262]) ).
tcf(c_351,plain,
sorti1(sK2_ax3_V(j(sK1_ax4_U))) = iPr_def_10,
inference(demodulation,[status(thm)],[c_326,c_143]) ).
tcf(c_352,plain,
op1(sK2_ax3_V(j(sK1_ax4_U)),sK2_ax3_V(j(sK1_ax4_U))) = j(sK1_ax4_U),
inference(demodulation,[status(thm)],[c_324,c_144]) ).
tcf(c_383,plain,
ifeq(iPr_def_10,iPr_def_10,sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))),iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_351,c_263]) ).
tcf(c_396,plain,
ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),iPr_def_10,ifeq2(sorti1(sK2_ax3_V(j(sK1_ax4_U))),iPr_def_10,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))) = h(j(sK1_ax4_U)),
inference(superposition,[status(thm)],[c_352,c_270]) ).
tcf(c_452,plain,
sorti2(h(sK2_ax3_V(j(sK1_ax4_U)))) = iPr_def_10,
inference(demodulation,[status(thm)],[c_383,c_143]) ).
tcf(c_479,plain,
op2(h(sK2_ax3_V(j(sK1_ax4_U))),h(sK2_ax3_V(j(sK1_ax4_U)))) = sK1_ax4_U,
inference(demodulation,[status(thm)],[c_396,c_144,c_300,c_351]) ).
tcf(c_664,plain,
tuple(sK1_ax4_U,sorti2(h(sK2_ax3_V(j(sK1_ax4_U))))) != iPr_def_11,
inference(superposition,[status(thm)],[c_479,c_138]) ).
tcf(c_950,plain,
$false,
inference(ground_joinability,[status(thm)],[c_664,c_261,c_452]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG069-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.38 % Computer : n002.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Fri Sep 25 04:44:13 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/5.42 Running UEQ theorem proving
% 0.15/5.42 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
% 0.15/5.43
% 0.15/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.43
% 0.15/5.43 % Detected problem language: tptp
% 0.15/5.45 % Proving...
% 1.77/6.29 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 1.77/6.29 % SZS status Started for theBenchmark.p
% 1.77/6.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.77/6.29
% 1.77/6.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.77/6.29
% 1.77/6.29 % ------ iProver source info
% 1.77/6.29
% 1.77/6.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.77/6.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.77/6.29 % git: non_committed_changes: false
% 1.77/6.29
% 1.77/6.29 % ------ Parsing...% successful
% 1.77/6.29
% 1.77/6.29
% 1.77/6.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.77/6.29
% 1.77/6.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.77/6.29
% 1.77/6.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.77/6.29
% 1.77/6.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 1.77/6.29 % ------ Proving...
% 1.77/6.29 % ------ Problem Properties
% 1.77/6.29
% 1.77/6.29 %
% 1.77/6.29 % clauses 16
% 1.77/6.29 % conjectures 6
% 1.77/6.29 % EPR 1
% 1.77/6.29 % Horn 16
% 1.77/6.29 % unary 16
% 1.77/6.29 % binary 0
% 1.77/6.29 % lits 16
% 1.77/6.29 % lits eq 16
% 1.77/6.29 % fd_pure 0
% 1.77/6.29 % fd_pseudo 0
% 1.77/6.29 % fd_cond 0
% 1.77/6.29 % fd_pseudo_cond 0
% 1.77/6.29 % AC symbols 0
% 1.77/6.29
% 1.77/6.29 % ------ Input Options Time Limit: Unbounded
% 1.77/6.29
% 1.77/6.29
% 1.77/6.29 % ------
% 1.77/6.29 % Current options:
% 1.77/6.29 % ------
% 1.77/6.29
% 1.77/6.29
% 1.77/6.29 %
% 1.77/6.29
% 1.77/6.29 % ------ Proving...
% 1.77/6.29 %
% 1.77/6.29
% 1.77/6.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.77/6.29
% 1.77/6.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.77/6.29
% 1.77/6.29
%------------------------------------------------------------------------------