%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL006-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n014.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 27.89s 4.78s
% Output : CNFRefutation 27.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of formulae : 54 ( 51 unt; 14 def)
% Number of atoms : 140 ( 51 equ)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 13 ( 10 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 15 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn 53 !; 0 ?; 47 :)
% 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,
! [X0] :
( fixed_point(X0)
| apply(X0,fixed_pt) != apply(fixed_pt,apply(X0,fixed_pt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f4,negated_conjecture,
~ fixed_point(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))))),
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,
! [X0: $i] :
( fixed_point(X0)
| ( apply(fixed_pt,apply(X0,fixed_pt)) != apply(X0,fixed_pt) ) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_56,negated_conjecture,
~ fixed_point(apply(apply(s,apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,apply(k,s)),k)),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))))),
inference(cnf_transformation,[],[f4]) ).
tcf(c_72,plain,
~ fixed_point(apply(apply(apply(s,s),apply(s,apply(apply(s,apply(k,s)),k))),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))))),
inference(demodulation,[status(thm)],[c_56,c_53]) ).
tcf(c_78,plain,
! [X0: $i] :
( ( apply(fixed_pt,apply(X0,fixed_pt)) != apply(X0,fixed_pt) )
| ( apply(apply(apply(s,s),apply(s,apply(apply(s,apply(k,s)),k))),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_72]) ).
tcf(c_79,plain,
apply(fixed_pt,apply(apply(apply(apply(s,s),apply(s,apply(apply(s,apply(k,s)),k))),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt)) != apply(apply(apply(apply(s,s),apply(s,apply(apply(s,apply(k,s)),k))),apply(k,apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)))),fixed_pt),
inference(unflattening,[status(thm)],[c_78]) ).
tcf(c_93,definition,
iPr_def_10 = apply(s,s),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_94,definition,
iPr_def_11 = apply(k,s),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_95,definition,
iPr_def_12 = apply(s,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_96,definition,
iPr_def_13 = apply(iPr_def_12,k),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_97,definition,
iPr_def_14 = apply(s,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_98,definition,
iPr_def_15 = apply(iPr_def_10,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_99,definition,
iPr_def_16 = apply(s,k),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_100,definition,
iPr_def_17 = apply(iPr_def_16,k),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_101,definition,
iPr_def_18 = apply(s,iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_102,definition,
iPr_def_19 = apply(iPr_def_18,iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_103,definition,
iPr_def_20 = apply(k,iPr_def_19),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_104,definition,
iPr_def_21 = apply(iPr_def_15,iPr_def_20),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_105,definition,
iPr_def_22 = apply(iPr_def_21,fixed_pt),
introduced(definition,[new_symbols(definition,[iPr_def_22])],[]) ).
tcf(c_106,definition,
iPr_def_23 = apply(fixed_pt,iPr_def_22),
introduced(definition,[new_symbols(definition,[iPr_def_23])],[]) ).
tcf(c_107,plain,
iPr_def_23 != iPr_def_22,
inference(demodulation,[status(thm)],[c_79,c_99,c_100,c_101,c_102,c_103,c_94,c_95,c_96,c_97,c_93,c_98,c_104,c_105,c_106]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_13,X0),apply(X1,X0)) = apply(apply(iPr_def_14,X1),X0),
inference(superposition,[status(thm)],[c_97,c_53]) ).
tcf(c_172,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_53,c_53]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(X0,X1),apply(apply(X2,X0),X1)) = apply(apply(apply(iPr_def_10,X2),X0),X1),
inference(light_normalisation,[status(thm)],[c_172,c_93]) ).
tcf(c_178,plain,
! [X0: $i] : apply(iPr_def_11,X0) = s,
inference(superposition,[status(thm)],[c_94,c_54]) ).
tcf(c_179,plain,
! [X0: $i] : apply(iPr_def_20,X0) = iPr_def_19,
inference(superposition,[status(thm)],[c_103,c_54]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i] : apply(apply(apply(s,k),X0),X1) = X1,
inference(superposition,[status(thm)],[c_54,c_53]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_16,X0),X1) = X1,
inference(light_normalisation,[status(thm)],[c_182,c_99]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i] : apply(apply(apply(s,iPr_def_11),X0),X1) = apply(s,apply(X0,X1)),
inference(superposition,[status(thm)],[c_178,c_53]) ).
tcf(c_187,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_12,X0),X1) = apply(s,apply(X0,X1)),
inference(light_normalisation,[status(thm)],[c_185,c_95]) ).
tcf(c_193,plain,
! [X0: $i] : apply(iPr_def_17,X0) = X0,
inference(superposition,[status(thm)],[c_100,c_183]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i] : apply(apply(apply(s,iPr_def_17),X0),X1) = apply(X1,apply(X0,X1)),
inference(superposition,[status(thm)],[c_193,c_53]) ).
tcf(c_200,plain,
! [X0: $i,X1: $i] : apply(X0,apply(X1,X0)) = apply(apply(iPr_def_18,X1),X0),
inference(light_normalisation,[status(thm)],[c_198,c_101]) ).
tcf(c_203,plain,
! [X0: $i] : apply(s,apply(k,X0)) = apply(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_96,c_187]) ).
tcf(c_210,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(k,X0),X1),apply(X2,X1)) = apply(apply(apply(iPr_def_13,X0),X2),X1),
inference(superposition,[status(thm)],[c_203,c_53]) ).
tcf(c_214,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(iPr_def_13,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(light_normalisation,[status(thm)],[c_210,c_54]) ).
tcf(c_243,plain,
! [X0: $i] : apply(X0,apply(iPr_def_17,X0)) = apply(iPr_def_19,X0),
inference(superposition,[status(thm)],[c_102,c_200]) ).
tcf(c_256,plain,
! [X0: $i] : apply(X0,X0) = apply(iPr_def_19,X0),
inference(light_normalisation,[status(thm)],[c_243,c_193]) ).
tcf(c_776,plain,
! [X0: $i] : apply(apply(iPr_def_13,X0),iPr_def_19) = apply(apply(iPr_def_14,iPr_def_20),X0),
inference(superposition,[status(thm)],[c_179,c_169]) ).
tcf(c_3364,plain,
! [X0: $i] : apply(apply(iPr_def_20,X0),apply(apply(iPr_def_13,X0),iPr_def_19)) = apply(apply(apply(iPr_def_10,iPr_def_14),iPr_def_20),X0),
inference(superposition,[status(thm)],[c_776,c_175]) ).
tcf(c_3568,plain,
! [X0: $i] : apply(iPr_def_19,apply(apply(iPr_def_13,X0),iPr_def_19)) = apply(iPr_def_21,X0),
inference(light_normalisation,[status(thm)],[c_3364,c_98,c_104,c_179]) ).
tcf(c_4242,plain,
! [X0: $i] : apply(iPr_def_19,apply(apply(iPr_def_14,iPr_def_20),X0)) = apply(iPr_def_21,X0),
inference(superposition,[status(thm)],[c_776,c_3568]) ).
tcf(c_4419,plain,
! [X0: $i,X1: $i] : apply(apply(apply(iPr_def_14,iPr_def_20),X0),X1) = apply(X0,apply(iPr_def_19,X1)),
inference(superposition,[status(thm)],[c_776,c_214]) ).
tcf(c_32791,plain,
! [X0: $i] : apply(X0,apply(iPr_def_19,apply(apply(iPr_def_14,iPr_def_20),X0))) = apply(iPr_def_19,apply(apply(iPr_def_14,iPr_def_20),X0)),
inference(superposition,[status(thm)],[c_4419,c_256]) ).
tcf(c_32817,plain,
! [X0: $i] : apply(X0,apply(iPr_def_21,X0)) = apply(iPr_def_21,X0),
inference(light_normalisation,[status(thm)],[c_32791,c_4242]) ).
tcf(c_32907,plain,
apply(fixed_pt,iPr_def_22) = iPr_def_22,
inference(superposition,[status(thm)],[c_105,c_32817]) ).
tcf(c_33166,plain,
iPr_def_22 = iPr_def_23,
inference(demodulation,[status(thm)],[c_106,c_32907]) ).
tcf(c_33172,plain,
iPr_def_22 != iPr_def_22,
inference(demodulation,[status(thm)],[c_107,c_33166]) ).
tcf(c_33173,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_33172]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL006-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 07:12:02 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 27.89/4.78 % SZS status Started for theBenchmark.p
% 27.89/4.78 % SZS status Unsatisfiable for theBenchmark.p
% 27.89/4.78
% 27.89/4.78 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 27.89/4.78
% 27.89/4.78 % ------ iProver source info
% 27.89/4.78
% 27.89/4.78 % git: date: 2026-07-19 20:42:38 +0200
% 27.89/4.78 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 27.89/4.78 % git: non_committed_changes: false
% 27.89/4.78
% 27.89/4.78 % ------ Parsing...% successful
% 27.89/4.78
% 27.89/4.78
% 27.89/4.78 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 27.89/4.78
% 27.89/4.78 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 27.89/4.78
% 27.89/4.78 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 27.89/4.78 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 27.89/4.78
% 27.89/4.78 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 27.89/4.78 % ------ Proving...
% 27.89/4.78 % ------ Problem Properties
% 27.89/4.78
% 27.89/4.78 %
% 27.89/4.78 % clauses 17
% 27.89/4.78 % conjectures 0
% 27.89/4.78 % EPR 1
% 27.89/4.78 % Horn 17
% 27.89/4.78 % unary 17
% 27.89/4.78 % binary 0
% 27.89/4.78 % lits 17
% 27.89/4.78 % lits eq 17
% 27.89/4.78 % fd_pure 0
% 27.89/4.78 % fd_pseudo 0
% 27.89/4.78 % fd_cond 0
% 27.89/4.78 % fd_pseudo_cond 0
% 27.89/4.78 % AC symbols 0
% 27.89/4.78
% 27.89/4.78 % ------ Schedule UEQ
% 27.89/4.78
% 27.89/4.78 % ------ Option_UEQ Time Limit: 10.
% 27.89/4.78
% 27.89/4.78
% 27.89/4.78 % ------
% 27.89/4.78 % Current options:
% 27.89/4.78 % ------
% 27.89/4.78
% 27.89/4.78
% 27.89/4.78 %
% 27.89/4.78
% 27.89/4.78 % ------ Proving...
% 27.89/4.78 %
% 27.89/4.78
% 27.89/4.78 % SZS status Unsatisfiable for theBenchmark.p
% 27.89/4.78
% 27.89/4.78 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 27.89/4.78
%------------------------------------------------------------------------------