%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL006-7 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n012.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 01:02:32 PM UTC 2026
% Result : Unsatisfiable 158.54s 21.23s
% Output : CNFRefutation 158.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 18
% Syntax : Number of formulae : 80 ( 80 unt; 14 def)
% Number of atoms : 212 ( 79 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 19 ( 17 usr; 15 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 107 ( 0 sgn 107 !; 0 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_definition) ).
fof(f2,axiom,
! [X0,X1] : apply(apply(k,X0),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_definition) ).
fof(f3,axiom,
strong_fixed_point = apply(apply(s,apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))))),apply(apply(s,apply(k,s)),k)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f4,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(X0,X1),apply(X2,X1)) = apply(apply(apply(s,X0),X2),X1),
inference(cnf_transformation,[],[f1]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] : apply(apply(k,X0),X1) = X0,
inference(cnf_transformation,[],[f2]) ).
tcf(c_55,plain,
apply(apply(s,apply(k,apply(apply(apply(s,s),apply(apply(s,k),k)),apply(apply(s,s),apply(s,k))))),apply(apply(s,apply(k,s)),k)) = strong_fixed_point,
inference(cnf_transformation,[],[f3]) ).
tcf(c_56,negated_conjecture,
apply(fixed_pt,apply(strong_fixed_point,fixed_pt)) != apply(strong_fixed_point,fixed_pt),
inference(cnf_transformation,[],[f4]) ).
tcf(c_70,definition,
iPr_def_10 = apply(strong_fixed_point,fixed_pt),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_71,definition,
iPr_def_11 = apply(fixed_pt,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_72,definition,
iPr_def_12 = apply(s,s),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_73,definition,
iPr_def_13 = apply(s,k),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_74,definition,
iPr_def_14 = apply(iPr_def_13,k),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_75,definition,
iPr_def_15 = apply(iPr_def_12,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_76,definition,
iPr_def_16 = apply(iPr_def_12,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_77,definition,
iPr_def_17 = apply(iPr_def_15,iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_78,definition,
iPr_def_18 = apply(k,iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_79,definition,
iPr_def_19 = apply(s,iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_80,definition,
iPr_def_20 = apply(k,s),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_81,definition,
iPr_def_21 = apply(s,iPr_def_20),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_82,definition,
iPr_def_22 = apply(iPr_def_21,k),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_83,definition,
iPr_def_23 = apply(iPr_def_19,iPr_def_22),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_84,negated_conjecture,
iPr_def_11 != iPr_def_10,
inference(demodulation,[status(thm)],[c_56,c_70,c_71]) ).
tcf(c_85,plain,
iPr_def_23 = strong_fixed_point,
inference(demodulation,[status(thm)],[c_55,c_80,c_81,c_82,c_76,c_73,c_74,c_72,c_75,c_77,c_78,c_79,c_83]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i] : apply(apply(k,X0),X1) = X0,
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(X0,X1),apply(X2,X1)) = apply(apply(apply(s,X0),X2),X1),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_143,plain,
apply(iPr_def_23,fixed_pt) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_70,c_85]) ).
tcf(c_144,plain,
! [X0: $i] : apply(iPr_def_20,X0) = s,
inference(superposition,[status(thm)],[c_80,c_86]) ).
tcf(c_145,plain,
! [X0: $i] : apply(iPr_def_18,X0) = iPr_def_17,
inference(superposition,[status(thm)],[c_78,c_86]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(s,X0),apply(k,X1)),X2) = apply(apply(X0,X2),X1),
inference(superposition,[status(thm)],[c_86,c_87]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i] : apply(apply(s,X0),apply(X1,X0)) = apply(apply(iPr_def_12,X1),X0),
inference(superposition,[status(thm)],[c_72,c_87]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_18,X0),apply(X1,X0)) = apply(apply(iPr_def_19,X1),X0),
inference(superposition,[status(thm)],[c_79,c_87]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_20,X0),apply(X1,X0)) = apply(apply(iPr_def_21,X1),X0),
inference(superposition,[status(thm)],[c_81,c_87]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(X0,X1),apply(apply(X2,X0),X1)) = apply(apply(apply(apply(s,s),X2),X0),X1),
inference(superposition,[status(thm)],[c_87,c_87]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i] : apply(apply(apply(s,k),X0),X1) = X1,
inference(superposition,[status(thm)],[c_87,c_86]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_13,X0),X1) = X1,
inference(demodulation,[status(thm)],[c_167,c_73]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_21,X0),X1) = apply(s,apply(X0,X1)),
inference(demodulation,[status(thm)],[c_163,c_144]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_19,X0),X1) = apply(iPr_def_17,apply(X0,X1)),
inference(demodulation,[status(thm)],[c_162,c_145]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(X0,X1),apply(apply(X2,X0),X1)) = apply(apply(apply(iPr_def_12,X2),X0),X1),
inference(demodulation,[status(thm)],[c_166,c_72]) ).
tcf(c_191,plain,
! [X0: $i] : apply(iPr_def_14,X0) = X0,
inference(superposition,[status(thm)],[c_74,c_170]) ).
tcf(c_192,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(s,apply(iPr_def_13,X0)),X1),X2) = apply(X2,apply(X1,X2)),
inference(superposition,[status(thm)],[c_170,c_87]) ).
tcf(c_193,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(s,X0),apply(iPr_def_13,X1)),X2) = apply(apply(X0,X2),X2),
inference(superposition,[status(thm)],[c_170,c_87]) ).
tcf(c_204,plain,
! [X0: $i] : apply(s,apply(k,X0)) = apply(iPr_def_22,X0),
inference(superposition,[status(thm)],[c_82,c_171]) ).
tcf(c_214,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(k,X0),X1),apply(X2,X1)) = apply(apply(apply(iPr_def_22,X0),X2),X1),
inference(superposition,[status(thm)],[c_204,c_87]) ).
tcf(c_219,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(iPr_def_22,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(demodulation,[status(thm)],[c_214,c_86]) ).
tcf(c_225,plain,
! [X0: $i] : apply(iPr_def_17,apply(iPr_def_22,X0)) = apply(iPr_def_23,X0),
inference(superposition,[status(thm)],[c_83,c_172]) ).
tcf(c_354,plain,
! [X0: $i] : apply(apply(s,X0),X0) = apply(apply(iPr_def_12,iPr_def_14),X0),
inference(superposition,[status(thm)],[c_191,c_160]) ).
tcf(c_380,plain,
! [X0: $i] : apply(apply(s,X0),X0) = apply(iPr_def_15,X0),
inference(demodulation,[status(thm)],[c_354,c_75]) ).
tcf(c_1103,plain,
! [X0: $i,X1: $i] : apply(apply(apply(k,X0),X1),X0) = apply(apply(iPr_def_15,apply(k,X0)),X1),
inference(superposition,[status(thm)],[c_380,c_156]) ).
tcf(c_1124,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_15,apply(k,X0)),X1) = apply(X0,X0),
inference(demodulation,[status(thm)],[c_1103,c_86]) ).
tcf(c_2120,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(iPr_def_15,apply(k,X0)),X1) = apply(apply(iPr_def_15,apply(k,X0)),X2),
inference(superposition,[status(thm)],[c_1124,c_1124]) ).
tcf(c_2126,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_15,apply(k,X0)),X1) = iPr_def_24(X0),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_24])],[c_2120]) ).
tcf(c_2135,plain,
! [X0: $i] : apply(X0,X0) = iPr_def_24(X0),
inference(demodulation,[status(thm)],[c_1124,c_2126]) ).
tcf(c_2258,plain,
! [X0: $i,X1: $i] : apply(apply(apply(s,X0),X0),X1) = iPr_def_24(apply(X0,X1)),
inference(superposition,[status(thm)],[c_2135,c_87]) ).
tcf(c_2314,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_15,X0),X1) = iPr_def_24(apply(X0,X1)),
inference(demodulation,[status(thm)],[c_2258,c_380]) ).
tcf(c_3282,plain,
! [X0: $i] : iPr_def_24(apply(iPr_def_16,X0)) = apply(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_77,c_2314]) ).
tcf(c_5595,plain,
! [X0: $i,X1: $i] : apply(apply(apply(iPr_def_12,iPr_def_13),X0),X1) = apply(apply(X0,X1),X1),
inference(superposition,[status(thm)],[c_170,c_176]) ).
tcf(c_5872,plain,
! [X0: $i,X1: $i] : apply(apply(X0,X1),X1) = apply(apply(iPr_def_16,X0),X1),
inference(demodulation,[status(thm)],[c_5595,c_76]) ).
tcf(c_6610,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : apply(apply(apply(s,apply(iPr_def_13,X0)),X1),X2) = apply(apply(apply(s,apply(iPr_def_13,X3)),X1),X2),
inference(superposition,[status(thm)],[c_192,c_192]) ).
tcf(c_6630,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(s,apply(iPr_def_13,X0)),X1),X2) = iPr_def_25(X1,X2),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_25])],[c_6610]) ).
tcf(c_6668,plain,
! [X0: $i,X1: $i] : apply(X0,apply(X1,X0)) = iPr_def_25(X1,X0),
inference(demodulation,[status(thm)],[c_192,c_6630]) ).
tcf(c_7071,plain,
apply(fixed_pt,iPr_def_10) = iPr_def_25(iPr_def_23,fixed_pt),
inference(superposition,[status(thm)],[c_143,c_6668]) ).
tcf(c_7323,plain,
iPr_def_25(iPr_def_23,fixed_pt) = iPr_def_11,
inference(demodulation,[status(thm)],[c_7071,c_71]) ).
tcf(c_9617,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : apply(apply(apply(s,X0),apply(iPr_def_13,X1)),X2) = apply(apply(apply(s,X0),apply(iPr_def_13,X3)),X2),
inference(superposition,[status(thm)],[c_193,c_193]) ).
tcf(c_9651,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(s,X0),apply(iPr_def_13,X1)),X2) = iPr_def_27(X0,X2),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_27])],[c_9617]) ).
tcf(c_9699,plain,
! [X0: $i,X1: $i] : apply(apply(X0,X1),X1) = iPr_def_27(X0,X1),
inference(demodulation,[status(thm)],[c_193,c_9651]) ).
tcf(c_15910,plain,
! [X0: $i] : apply(iPr_def_17,X0) = iPr_def_27(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_145,c_9699]) ).
tcf(c_16112,plain,
! [X0: $i,X1: $i] : apply(X0,apply(X1,X1)) = iPr_def_27(apply(iPr_def_22,X0),X1),
inference(superposition,[status(thm)],[c_9699,c_219]) ).
tcf(c_16180,plain,
! [X0: $i,X1: $i] : iPr_def_27(apply(iPr_def_22,X0),X1) = apply(X0,iPr_def_24(X1)),
inference(demodulation,[status(thm)],[c_16112,c_2135]) ).
tcf(c_16294,plain,
! [X0: $i] : iPr_def_24(apply(iPr_def_16,X0)) = iPr_def_27(iPr_def_18,X0),
inference(demodulation,[status(thm)],[c_3282,c_15910]) ).
tcf(c_16304,plain,
! [X0: $i] : iPr_def_27(iPr_def_18,apply(iPr_def_22,X0)) = apply(iPr_def_23,X0),
inference(demodulation,[status(thm)],[c_225,c_15910]) ).
tcf(c_82635,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_16,X0),X1) = iPr_def_27(X0,X1),
inference(light_normalisation,[status(thm)],[c_5872,c_9699]) ).
tcf(c_82756,plain,
! [X0: $i] : iPr_def_27(X0,apply(iPr_def_16,X0)) = iPr_def_24(apply(iPr_def_16,X0)),
inference(superposition,[status(thm)],[c_82635,c_2135]) ).
tcf(c_82770,plain,
! [X0: $i] : iPr_def_27(X0,apply(iPr_def_16,X0)) = iPr_def_27(iPr_def_18,X0),
inference(demodulation,[status(thm)],[c_82756,c_16294]) ).
tcf(c_87981,plain,
! [X0: $i] : apply(X0,iPr_def_24(apply(iPr_def_16,apply(iPr_def_22,X0)))) = iPr_def_27(iPr_def_18,apply(iPr_def_22,X0)),
inference(superposition,[status(thm)],[c_82770,c_16180]) ).
tcf(c_88085,plain,
! [X0: $i] : apply(iPr_def_23,X0) = iPr_def_25(iPr_def_23,X0),
inference(demodulation,[status(thm)],[c_87981,c_6668,c_16294,c_16304]) ).
tcf(c_88100,plain,
iPr_def_25(iPr_def_23,fixed_pt) = iPr_def_10,
inference(demodulation,[status(thm)],[c_143,c_88085]) ).
tcf(c_88111,plain,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_7323,c_88100]) ).
tcf(c_88124,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_84,c_88111]) ).
tcf(c_88125,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_88124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL006-7 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n012.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 : Fri Sep 25 07:11:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.38 Running UEQ theorem proving
% 0.09/0.38 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.38
% 0.09/0.38 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.38
% 0.09/0.38 % Detected problem language: tptp
% 0.09/0.39 % Proving...
% 158.54/21.23 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 158.54/21.23 % SZS status Started for theBenchmark.p
% 158.54/21.23 % SZS status Unsatisfiable for theBenchmark.p
% 158.54/21.23
% 158.54/21.23 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 158.54/21.23
% 158.54/21.23 % ------ iProver source info
% 158.54/21.23
% 158.54/21.23 % git: date: 2026-07-19 20:42:38 +0200
% 158.54/21.23 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 158.54/21.23 % git: non_committed_changes: false
% 158.54/21.23
% 158.54/21.23 % ------ Parsing...% successful
% 158.54/21.23
% 158.54/21.23
% 158.54/21.23 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 158.54/21.23
% 158.54/21.23 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 158.54/21.23
% 158.54/21.23 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 158.54/21.23
% 158.54/21.23 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 158.54/21.23 % ------ Proving...
% 158.54/21.23 % ------ Problem Properties
% 158.54/21.23
% 158.54/21.23 %
% 158.54/21.23 % clauses 18
% 158.54/21.23 % conjectures 1
% 158.54/21.23 % EPR 2
% 158.54/21.23 % Horn 18
% 158.54/21.23 % unary 18
% 158.54/21.23 % binary 0
% 158.54/21.23 % lits 18
% 158.54/21.23 % lits eq 18
% 158.54/21.23 % fd_pure 0
% 158.54/21.23 % fd_pseudo 0
% 158.54/21.23 % fd_cond 0
% 158.54/21.23 % fd_pseudo_cond 0
% 158.54/21.23 % AC symbols 0
% 158.54/21.23
% 158.54/21.23 % ------ Input Options Time Limit: Unbounded
% 158.54/21.23
% 158.54/21.23
% 158.54/21.23 % ------
% 158.54/21.23 % Current options:
% 158.54/21.23 % ------
% 158.54/21.23
% 158.54/21.23
% 158.54/21.23 %
% 158.54/21.23
% 158.54/21.23 % ------ Proving...
% 158.54/21.23 %
% 158.54/21.23
% 158.54/21.23 % SZS status Unsatisfiable for theBenchmark.p
% 158.54/21.23
% 158.54/21.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 158.54/21.23
% 158.54/21.23
%------------------------------------------------------------------------------