%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL006-5 : 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 : n011.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 12.06s 6.23s
% Output : CNFRefutation 12.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 21
% Syntax : Number of formulae : 71 ( 71 unt; 17 def)
% Number of atoms : 170 ( 70 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 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; 18 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 79 !; 0 ?; 74 :)
% 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(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(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(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(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,k),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_73,definition,
iPr_def_13 = apply(iPr_def_12,k),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_74,definition,
iPr_def_14 = apply(s,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_75,definition,
iPr_def_15 = apply(iPr_def_14,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_76,definition,
iPr_def_16 = apply(k,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_77,definition,
iPr_def_17 = apply(s,iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_78,definition,
iPr_def_18 = apply(s,s),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_79,definition,
iPr_def_19 = apply(iPr_def_18,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_80,definition,
iPr_def_20 = apply(k,iPr_def_19),
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(k,s),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_83,definition,
iPr_def_23 = apply(s,iPr_def_22),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_84,definition,
iPr_def_24 = apply(iPr_def_23,k),
introduced(definition,[new_symbols(definition,[iPr_def_24])],[]) ).
tcf(c_85,definition,
iPr_def_25 = apply(iPr_def_21,iPr_def_24),
introduced(definition,[new_symbols(definition,[iPr_def_25])],[]) ).
tcf(c_86,definition,
iPr_def_26 = apply(iPr_def_17,iPr_def_25),
introduced(definition,[new_symbols(definition,[iPr_def_26])],[]) ).
tcf(c_87,negated_conjecture,
iPr_def_11 != iPr_def_10,
inference(demodulation,[status(thm)],[c_56,c_70,c_71]) ).
tcf(c_88,plain,
iPr_def_26 = strong_fixed_point,
inference(demodulation,[status(thm)],[c_55,c_82,c_83,c_84,c_78,c_79,c_80,c_81,c_85,c_72,c_73,c_74,c_75,c_76,c_77,c_86]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] : apply(apply(k,X0),X1) = X0,
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_90,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_185,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_90,c_90]) ).
tcf(c_197,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(X0,X1),apply(apply(X2,X0),X1)) = apply(apply(apply(iPr_def_18,X2),X0),X1),
inference(demodulation,[status(thm)],[c_185,c_78]) ).
tcf(c_1425,plain,
! [X0: $i] : apply(iPr_def_22,X0) = s,
inference(superposition,[status(thm)],[c_82,c_89]) ).
tcf(c_1427,plain,
! [X0: $i] : apply(iPr_def_20,X0) = iPr_def_19,
inference(superposition,[status(thm)],[c_80,c_89]) ).
tcf(c_1446,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_90]) ).
tcf(c_1447,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_22,X0),apply(X1,X0)) = apply(apply(iPr_def_23,X1),X0),
inference(superposition,[status(thm)],[c_83,c_90]) ).
tcf(c_1451,plain,
! [X0: $i,X1: $i] : apply(apply(apply(s,k),X0),X1) = X1,
inference(superposition,[status(thm)],[c_90,c_89]) ).
tcf(c_1454,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_12,X0),X1) = X1,
inference(demodulation,[status(thm)],[c_1451,c_72]) ).
tcf(c_1455,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_23,X0),X1) = apply(s,apply(X0,X1)),
inference(demodulation,[status(thm)],[c_1447,c_1425]) ).
tcf(c_1456,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_21,X0),X1) = apply(iPr_def_19,apply(X0,X1)),
inference(demodulation,[status(thm)],[c_1446,c_1427]) ).
tcf(c_1463,plain,
! [X0: $i] : apply(iPr_def_13,X0) = X0,
inference(superposition,[status(thm)],[c_73,c_1454]) ).
tcf(c_1467,plain,
! [X0: $i,X1: $i] : apply(apply(apply(s,iPr_def_13),X0),X1) = apply(X1,apply(X0,X1)),
inference(superposition,[status(thm)],[c_1463,c_90]) ).
tcf(c_1469,plain,
! [X0: $i,X1: $i] : apply(X0,apply(X1,X0)) = apply(apply(iPr_def_14,X1),X0),
inference(demodulation,[status(thm)],[c_1467,c_74]) ).
tcf(c_1471,plain,
! [X0: $i] : apply(s,apply(k,X0)) = apply(iPr_def_24,X0),
inference(superposition,[status(thm)],[c_84,c_1455]) ).
tcf(c_1478,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(k,X0),X1),apply(X2,X1)) = apply(apply(apply(iPr_def_24,X0),X2),X1),
inference(superposition,[status(thm)],[c_1471,c_90]) ).
tcf(c_1484,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(iPr_def_24,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(demodulation,[status(thm)],[c_1478,c_89]) ).
tcf(c_1487,plain,
! [X0: $i] : apply(iPr_def_19,apply(iPr_def_24,X0)) = apply(iPr_def_25,X0),
inference(superposition,[status(thm)],[c_85,c_1456]) ).
tcf(c_1544,plain,
! [X0: $i] : apply(X0,apply(iPr_def_13,X0)) = apply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_75,c_1469]) ).
tcf(c_1559,plain,
! [X0: $i] : apply(X0,X0) = apply(iPr_def_15,X0),
inference(demodulation,[status(thm)],[c_1544,c_1463]) ).
tcf(c_2952,plain,
! [X0: $i,X1: $i] : apply(apply(apply(iPr_def_18,iPr_def_12),X0),X1) = apply(apply(X0,X1),X1),
inference(superposition,[status(thm)],[c_1454,c_197]) ).
tcf(c_3150,plain,
! [X0: $i,X1: $i] : apply(apply(X0,X1),X1) = apply(apply(iPr_def_19,X0),X1),
inference(demodulation,[status(thm)],[c_2952,c_79]) ).
tcf(c_5412,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_19,apply(iPr_def_24,X0)),X1) = apply(X0,apply(X1,X1)),
inference(superposition,[status(thm)],[c_3150,c_1484]) ).
tcf(c_5452,plain,
! [X0: $i,X1: $i] : apply(X0,apply(X1,X1)) = apply(apply(iPr_def_25,X0),X1),
inference(demodulation,[status(thm)],[c_5412,c_1487]) ).
tcf(c_9852,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_25,X0),X1) = apply(X0,apply(iPr_def_15,X1)),
inference(superposition,[status(thm)],[c_1559,c_5452]) ).
tcf(c_20390,plain,
apply(iPr_def_26,fixed_pt) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_70,c_88]) ).
tcf(c_20392,plain,
! [X0: $i] : apply(iPr_def_16,X0) = iPr_def_15,
inference(superposition,[status(thm)],[c_76,c_89]) ).
tcf(c_20415,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_16,X0),apply(X1,X0)) = apply(apply(iPr_def_17,X1),X0),
inference(superposition,[status(thm)],[c_77,c_90]) ).
tcf(c_20421,plain,
! [X0: $i,X1: $i] : apply(apply(apply(s,k),X0),X1) = X1,
inference(superposition,[status(thm)],[c_90,c_89]) ).
tcf(c_20425,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_12,X0),X1) = X1,
inference(demodulation,[status(thm)],[c_20421,c_72]) ).
tcf(c_20428,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_17,X0),X1) = apply(iPr_def_15,apply(X0,X1)),
inference(demodulation,[status(thm)],[c_20415,c_20392]) ).
tcf(c_20434,plain,
! [X0: $i] : apply(iPr_def_13,X0) = X0,
inference(superposition,[status(thm)],[c_73,c_20425]) ).
tcf(c_20438,plain,
! [X0: $i,X1: $i] : apply(apply(apply(s,iPr_def_13),X0),X1) = apply(X1,apply(X0,X1)),
inference(superposition,[status(thm)],[c_20434,c_90]) ).
tcf(c_20440,plain,
! [X0: $i,X1: $i] : apply(X0,apply(X1,X0)) = apply(apply(iPr_def_14,X1),X0),
inference(demodulation,[status(thm)],[c_20438,c_74]) ).
tcf(c_20472,plain,
! [X0: $i] : apply(iPr_def_15,apply(iPr_def_25,X0)) = apply(iPr_def_26,X0),
inference(superposition,[status(thm)],[c_86,c_20428]) ).
tcf(c_20521,plain,
! [X0: $i] : apply(X0,apply(iPr_def_13,X0)) = apply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_75,c_20440]) ).
tcf(c_20537,plain,
! [X0: $i] : apply(X0,X0) = apply(iPr_def_15,X0),
inference(demodulation,[status(thm)],[c_20521,c_20434]) ).
tcf(c_20582,plain,
! [X0: $i] : apply(X0,apply(iPr_def_15,apply(iPr_def_25,X0))) = apply(iPr_def_15,apply(iPr_def_25,X0)),
inference(superposition,[status(thm)],[c_20537,c_9852]) ).
tcf(c_20586,plain,
! [X0: $i] : apply(X0,apply(iPr_def_26,X0)) = apply(iPr_def_26,X0),
inference(demodulation,[status(thm)],[c_20582,c_20472]) ).
tcf(c_20695,plain,
apply(fixed_pt,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_20390,c_20586]) ).
tcf(c_20743,plain,
iPr_def_10 = iPr_def_11,
inference(demodulation,[status(thm)],[c_71,c_20695]) ).
tcf(c_20744,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_87,c_20743]) ).
tcf(c_20745,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_20744]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL006-5 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 07:11:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 Running UEQ theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 12.06/6.23 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 12.06/6.23 % SZS status Started for theBenchmark.p
% 12.06/6.23 % SZS status Unsatisfiable for theBenchmark.p
% 12.06/6.23
% 12.06/6.23 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 12.06/6.23
% 12.06/6.23 % ------ iProver source info
% 12.06/6.23
% 12.06/6.23 % git: date: 2026-07-19 20:42:38 +0200
% 12.06/6.23 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 12.06/6.23 % git: non_committed_changes: false
% 12.06/6.23
% 12.06/6.23 % ------ Parsing...% successful
% 12.06/6.23
% 12.06/6.23
% 12.06/6.23 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 12.06/6.23
% 12.06/6.23 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 12.06/6.23
% 12.06/6.23 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 12.06/6.23
% 12.06/6.23 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 12.06/6.23 % ------ Proving...
% 12.06/6.23 % ------ Problem Properties
% 12.06/6.23
% 12.06/6.23 %
% 12.06/6.23 % clauses 21
% 12.06/6.23 % conjectures 1
% 12.06/6.23 % EPR 2
% 12.06/6.23 % Horn 21
% 12.06/6.23 % unary 21
% 12.06/6.23 % binary 0
% 12.06/6.23 % lits 21
% 12.06/6.23 % lits eq 21
% 12.06/6.23 % fd_pure 0
% 12.06/6.23 % fd_pseudo 0
% 12.06/6.23 % fd_cond 0
% 12.06/6.23 % fd_pseudo_cond 0
% 12.06/6.23 % AC symbols 0
% 12.06/6.23
% 12.06/6.23 % ------ Input Options Time Limit: Unbounded
% 12.06/6.23
% 12.06/6.23
% 12.06/6.23 % ------
% 12.06/6.23 % Current options:
% 12.06/6.23 % ------
% 12.06/6.23
% 12.06/6.23
% 12.06/6.23 %
% 12.06/6.23
% 12.06/6.23 % ------ Proving...
% 12.06/6.23 %
% 12.06/6.23
% 12.06/6.23 % SZS status Unsatisfiable for theBenchmark.p
% 12.06/6.23
% 12.06/6.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 12.06/6.23
% 12.06/6.23
%------------------------------------------------------------------------------