%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL042-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 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 : Fri Sep 25 02:05:29 PM UTC 2026
% Result : Unsatisfiable 4.17s 3.75s
% Output : CNFRefutation 4.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 74 ( 74 unt; 7 def)
% Number of atoms : 129 ( 73 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 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 : 9 ( 7 usr; 8 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 100 ( 0 sgn 100 !; 0 ?; 69 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X0,X1] : ifeq(is_a_theorem(implies(X0,X1)),true,ifeq(is_a_theorem(X0),true,is_a_theorem(X1),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
fof(f3,plain,
! [X0,X1] : true = ifeq(is_a_theorem(implies(X0,X1)),true,ifeq(is_a_theorem(X0),true,is_a_theorem(X1),true),true),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_3) ).
fof(f5,plain,
! [X0,X1] : true = is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(reorient_equations,[],[f4]) ).
fof(f6,axiom,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_18) ).
fof(f7,plain,
! [X0,X1] : true = is_a_theorem(implies(X0,implies(X1,X0))),
inference(reorient_equations,[],[f6]) ).
fof(f8,axiom,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2)))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_21) ).
fof(f9,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2)))),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
! [X2,X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_22) ).
fof(f11,plain,
! [X2,X0,X1] : true = is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))),
inference(reorient_equations,[],[f10]) ).
fof(f12,axiom,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X1),X1))) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_54) ).
fof(f13,plain,
! [X0,X1] : true = is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X1),X1))),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
is_a_theorem(implies(implies(a,implies(b,c)),implies(implies(a,b),implies(a,c)))) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_35) ).
fof(f15,plain,
true != is_a_theorem(implies(implies(a,implies(b,c)),implies(implies(a,b),implies(a,c)))),
inference(reorient_equations,[],[f14]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] : ifeq(is_a_theorem(implies(X0,X1)),true,ifeq(is_a_theorem(X0),true,is_a_theorem(X1),true),true) = true,
inference(cnf_transformation,[],[f3]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(not(X0),X1))) = true,
inference(cnf_transformation,[],[f5]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(X1,X0))) = true,
inference(cnf_transformation,[],[f7]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2)))) = true,
inference(cnf_transformation,[],[f9]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))) = true,
inference(cnf_transformation,[],[f11]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X1),X1))) = true,
inference(cnf_transformation,[],[f13]) ).
tcf(c_64,negated_conjecture,
is_a_theorem(implies(implies(a,implies(b,c)),implies(implies(a,b),implies(a,c)))) != true,
inference(cnf_transformation,[],[f15]) ).
tcf(c_93,definition,
iPr_def_10 = implies(b,c),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_94,definition,
iPr_def_11 = implies(a,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_95,definition,
iPr_def_12 = implies(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_96,definition,
iPr_def_13 = implies(a,c),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_97,definition,
iPr_def_14 = implies(iPr_def_12,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_98,definition,
iPr_def_15 = implies(iPr_def_11,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_99,definition,
iPr_def_16 = is_a_theorem(iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_100,negated_conjecture,
iPr_def_16 != true,
inference(demodulation,[status(thm)],[c_64,c_96,c_95,c_97,c_93,c_94,c_98,c_99]) ).
tcf(c_1610,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(true,true,ifeq(is_a_theorem(implies(X0,X1)),true,is_a_theorem(implies(implies(X2,X0),implies(X2,X1))),true),true) = true,
inference(superposition,[status(thm)],[c_62,c_58]) ).
tcf(c_1613,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(is_a_theorem(implies(X0,X1)),true,is_a_theorem(implies(implies(X2,X0),implies(X2,X1))),true) = true,
inference(demodulation,[status(thm)],[c_1610,c_57]) ).
tcf(c_1623,plain,
! [X0: $i] : ifeq(is_a_theorem(implies(X0,iPr_def_15)),true,ifeq(is_a_theorem(X0),true,iPr_def_16,true),true) = true,
inference(superposition,[status(thm)],[c_99,c_58]) ).
tcf(c_1635,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(is_a_theorem(implies(implies(X0,implies(not(X0),X1)),X2)),true,ifeq(true,true,is_a_theorem(X2),true),true) = true,
inference(superposition,[status(thm)],[c_59,c_58]) ).
tcf(c_1641,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(is_a_theorem(implies(implies(X0,implies(not(X0),X1)),X2)),true,is_a_theorem(X2),true) = true,
inference(demodulation,[status(thm)],[c_1635,c_57]) ).
tcf(c_1700,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(true,true,is_a_theorem(implies(implies(X0,X1),implies(X0,implies(X2,X1)))),true) = true,
inference(superposition,[status(thm)],[c_60,c_1613]) ).
tcf(c_1701,plain,
! [X0: $i,X1: $i] : ifeq(true,true,ifeq(is_a_theorem(X0),true,is_a_theorem(implies(X1,X0)),true),true) = true,
inference(superposition,[status(thm)],[c_60,c_58]) ).
tcf(c_1714,plain,
! [X0: $i,X1: $i] : ifeq(is_a_theorem(X0),true,is_a_theorem(implies(X1,X0)),true) = true,
inference(demodulation,[status(thm)],[c_1701,c_57]) ).
tcf(c_1715,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),implies(X0,implies(X2,X1)))) = true,
inference(demodulation,[status(thm)],[c_1700,c_57]) ).
tcf(c_1727,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(true,true,ifeq(is_a_theorem(implies(X0,X1)),true,is_a_theorem(implies(X0,implies(X2,X1))),true),true) = true,
inference(superposition,[status(thm)],[c_1715,c_58]) ).
tcf(c_1739,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(is_a_theorem(implies(X0,X1)),true,is_a_theorem(implies(X0,implies(X2,X1))),true) = true,
inference(demodulation,[status(thm)],[c_1727,c_57]) ).
tcf(c_1909,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(true,true,ifeq(is_a_theorem(implies(X0,implies(X1,X2))),true,is_a_theorem(implies(X1,implies(X0,X2))),true),true) = true,
inference(superposition,[status(thm)],[c_61,c_58]) ).
tcf(c_1918,plain,
! [X0: $i,X1: $i] : ifeq(true,true,is_a_theorem(implies(not(X0),implies(X0,X1))),true) = true,
inference(superposition,[status(thm)],[c_61,c_1641]) ).
tcf(c_1924,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(not(X0),implies(X0,X1))) = true,
inference(demodulation,[status(thm)],[c_1918,c_57]) ).
tcf(c_1925,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(is_a_theorem(implies(X0,implies(X1,X2))),true,is_a_theorem(implies(X1,implies(X0,X2))),true) = true,
inference(demodulation,[status(thm)],[c_1909,c_57]) ).
tcf(c_2078,plain,
! [X0: $i,X1: $i] : ifeq(true,true,ifeq(is_a_theorem(implies(X0,X1)),true,is_a_theorem(implies(implies(not(X0),X1),X1)),true),true) = true,
inference(superposition,[status(thm)],[c_63,c_58]) ).
tcf(c_2093,plain,
! [X0: $i,X1: $i] : ifeq(is_a_theorem(implies(X0,X1)),true,is_a_theorem(implies(implies(not(X0),X1),X1)),true) = true,
inference(demodulation,[status(thm)],[c_2078,c_57]) ).
tcf(c_2309,plain,
! [X0: $i] : is_a_theorem(implies(iPr_def_10,implies(implies(X0,b),implies(X0,c)))) = true,
inference(superposition,[status(thm)],[c_93,c_62]) ).
tcf(c_3240,plain,
is_a_theorem(implies(iPr_def_10,implies(iPr_def_12,implies(a,c)))) = true,
inference(superposition,[status(thm)],[c_95,c_2309]) ).
tcf(c_3242,plain,
is_a_theorem(implies(iPr_def_10,iPr_def_14)) = true,
inference(light_normalisation,[status(thm)],[c_3240,c_96,c_97]) ).
tcf(c_3323,plain,
! [X0: $i] : ifeq(true,true,is_a_theorem(implies(implies(X0,iPr_def_10),implies(X0,iPr_def_14))),true) = true,
inference(superposition,[status(thm)],[c_3242,c_1613]) ).
tcf(c_3335,plain,
! [X0: $i] : is_a_theorem(implies(implies(X0,iPr_def_10),implies(X0,iPr_def_14))) = true,
inference(demodulation,[status(thm)],[c_3323,c_57]) ).
tcf(c_3787,plain,
is_a_theorem(implies(not(a),iPr_def_13)) = true,
inference(superposition,[status(thm)],[c_96,c_1924]) ).
tcf(c_18300,plain,
is_a_theorem(implies(iPr_def_11,implies(a,iPr_def_14))) = true,
inference(superposition,[status(thm)],[c_94,c_3335]) ).
tcf(c_18966,plain,
ifeq(true,true,is_a_theorem(implies(a,implies(iPr_def_11,iPr_def_14))),true) = true,
inference(superposition,[status(thm)],[c_18300,c_1925]) ).
tcf(c_18968,plain,
is_a_theorem(implies(a,implies(iPr_def_11,iPr_def_14))) = true,
inference(demodulation,[status(thm)],[c_18966,c_57]) ).
tcf(c_18969,plain,
is_a_theorem(implies(a,iPr_def_15)) = true,
inference(light_normalisation,[status(thm)],[c_18968,c_98]) ).
tcf(c_19039,plain,
ifeq(true,true,is_a_theorem(implies(implies(not(a),iPr_def_15),iPr_def_15)),true) = true,
inference(superposition,[status(thm)],[c_18969,c_2093]) ).
tcf(c_19070,plain,
is_a_theorem(implies(implies(not(a),iPr_def_15),iPr_def_15)) = true,
inference(demodulation,[status(thm)],[c_19039,c_57]) ).
tcf(c_27130,plain,
! [X0: $i] : ifeq(true,true,is_a_theorem(implies(X0,implies(not(a),iPr_def_13))),true) = true,
inference(superposition,[status(thm)],[c_3787,c_1714]) ).
tcf(c_27431,plain,
! [X0: $i] : is_a_theorem(implies(X0,implies(not(a),iPr_def_13))) = true,
inference(demodulation,[status(thm)],[c_27130,c_57]) ).
tcf(c_35891,plain,
! [X0: $i] : ifeq(true,true,is_a_theorem(implies(not(a),implies(X0,iPr_def_13))),true) = true,
inference(superposition,[status(thm)],[c_27431,c_1925]) ).
tcf(c_35924,plain,
! [X0: $i] : is_a_theorem(implies(not(a),implies(X0,iPr_def_13))) = true,
inference(demodulation,[status(thm)],[c_35891,c_57]) ).
tcf(c_42333,plain,
is_a_theorem(implies(not(a),iPr_def_14)) = true,
inference(superposition,[status(thm)],[c_97,c_35924]) ).
tcf(c_43504,plain,
! [X0: $i] : ifeq(true,true,is_a_theorem(implies(not(a),implies(X0,iPr_def_14))),true) = true,
inference(superposition,[status(thm)],[c_42333,c_1739]) ).
tcf(c_43555,plain,
! [X0: $i] : is_a_theorem(implies(not(a),implies(X0,iPr_def_14))) = true,
inference(demodulation,[status(thm)],[c_43504,c_57]) ).
tcf(c_47366,plain,
is_a_theorem(implies(not(a),iPr_def_15)) = true,
inference(superposition,[status(thm)],[c_98,c_43555]) ).
tcf(c_49281,plain,
ifeq(is_a_theorem(implies(implies(not(a),iPr_def_15),iPr_def_15)),true,ifeq(true,true,iPr_def_16,true),true) = true,
inference(superposition,[status(thm)],[c_47366,c_1623]) ).
tcf(c_49320,plain,
ifeq(is_a_theorem(implies(implies(not(a),iPr_def_15),iPr_def_15)),true,iPr_def_16,true) = true,
inference(demodulation,[status(thm)],[c_49281,c_57]) ).
tcf(c_49321,plain,
ifeq(true,true,iPr_def_16,true) = true,
inference(light_normalisation,[status(thm)],[c_49320,c_19070]) ).
tcf(c_49323,plain,
true = iPr_def_16,
inference(superposition,[status(thm)],[c_57,c_49321]) ).
tcf(c_49704,plain,
iPr_def_16 != iPr_def_16,
inference(demodulation,[status(thm)],[c_100,c_49323]) ).
tcf(c_49707,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_49704]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL042-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n018.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 21:44:32 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running UEQ theorem proving
% 0.14/0.40 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 4.17/3.75 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 4.17/3.75 % SZS status Started for theBenchmark.p
% 4.17/3.75 % SZS status Unsatisfiable for theBenchmark.p
% 4.17/3.75
% 4.17/3.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.17/3.75
% 4.17/3.75 % ------ iProver source info
% 4.17/3.75
% 4.17/3.75 % git: date: 2026-07-19 20:42:38 +0200
% 4.17/3.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.17/3.75 % git: non_committed_changes: false
% 4.17/3.75
% 4.17/3.75 % ------ Parsing...% successful
% 4.17/3.75
% 4.17/3.75
% 4.17/3.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.17/3.75
% 4.17/3.75 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 4.17/3.75
% 4.17/3.75 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.17/3.75
% 4.17/3.75 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 4.17/3.75 % ------ Proving...
% 4.17/3.75 % ------ Problem Properties
% 4.17/3.75
% 4.17/3.75 %
% 4.17/3.75 % clauses 15
% 4.17/3.75 % conjectures 1
% 4.17/3.75 % EPR 1
% 4.17/3.75 % Horn 15
% 4.17/3.75 % unary 15
% 4.17/3.75 % binary 0
% 4.17/3.75 % lits 15
% 4.17/3.75 % lits eq 15
% 4.17/3.75 % fd_pure 0
% 4.17/3.75 % fd_pseudo 0
% 4.17/3.75 % fd_cond 0
% 4.17/3.75 % fd_pseudo_cond 0
% 4.17/3.75 % AC symbols 0
% 4.17/3.75
% 4.17/3.75 % ------ Input Options Time Limit: Unbounded
% 4.17/3.75
% 4.17/3.75
% 4.17/3.75 % ------
% 4.17/3.75 % Current options:
% 4.17/3.75 % ------
% 4.17/3.75
% 4.17/3.75
% 4.17/3.75 %
% 4.17/3.75
% 4.17/3.75 % ------ Proving...
% 4.17/3.75 %
% 4.17/3.75
% 4.17/3.75 % SZS status Unsatisfiable for theBenchmark.p
% 4.17/3.75
% 4.17/3.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.17/3.75
% 4.17/3.75
%------------------------------------------------------------------------------