%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL006-2 : 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 : n013.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 01:02:31 PM UTC 2026
% Result : Unsatisfiable 6.03s 1.70s
% Output : CNFRefutation 6.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 45 ( 42 unt; 11 def)
% Number of atoms : 102 ( 43 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 : 10 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 42 !; 0 ?; 36 :)
% 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(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),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(k,apply(apply(s,s),apply(s,k)))),apply(apply(s,apply(k,s)),k)))),
inference(cnf_transformation,[],[f4]) ).
tcf(c_77,plain,
! [X0: $i] :
( ( apply(fixed_pt,apply(X0,fixed_pt)) != apply(X0,fixed_pt) )
| ( 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))) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_56]) ).
tcf(c_78,plain,
apply(fixed_pt,apply(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))),fixed_pt)) != apply(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))),fixed_pt),
inference(unflattening,[status(thm)],[c_77]) ).
tcf(c_89,plain,
apply(fixed_pt,apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt))))) != apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),apply(apply(apply(s,s),apply(s,k)),apply(s,apply(k,fixed_pt)))),
inference(demodulation,[status(thm)],[c_78,c_53,c_54]) ).
tcf(c_93,definition,
iPr_def_10 = apply(s,k),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_94,definition,
iPr_def_11 = apply(iPr_def_10,k),
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,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_97,definition,
iPr_def_14 = apply(s,s),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_98,definition,
iPr_def_15 = apply(iPr_def_14,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_99,definition,
iPr_def_16 = apply(k,fixed_pt),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_100,definition,
iPr_def_17 = apply(s,iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_101,definition,
iPr_def_18 = apply(iPr_def_15,iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_102,definition,
iPr_def_19 = apply(iPr_def_13,iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_103,definition,
iPr_def_20 = apply(fixed_pt,iPr_def_19),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_104,plain,
iPr_def_20 != iPr_def_19,
inference(demodulation,[status(thm)],[c_89,c_99,c_100,c_97,c_98,c_101,c_93,c_94,c_95,c_96,c_102,c_103]) ).
tcf(c_162,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_165,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(X0,X1),apply(apply(X2,X0),X1)) = apply(apply(apply(iPr_def_14,X2),X0),X1),
inference(light_normalisation,[status(thm)],[c_162,c_97]) ).
tcf(c_168,plain,
! [X0: $i] : apply(iPr_def_16,X0) = fixed_pt,
inference(superposition,[status(thm)],[c_99,c_54]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i] : apply(apply(apply(s,k),X0),X1) = X1,
inference(superposition,[status(thm)],[c_54,c_53]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_10,X0),X1) = X1,
inference(light_normalisation,[status(thm)],[c_171,c_93]) ).
tcf(c_174,plain,
! [X0: $i,X1: $i] : apply(apply(apply(s,iPr_def_16),X0),X1) = apply(fixed_pt,apply(X0,X1)),
inference(superposition,[status(thm)],[c_168,c_53]) ).
tcf(c_176,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_17,X0),X1) = apply(fixed_pt,apply(X0,X1)),
inference(light_normalisation,[status(thm)],[c_174,c_100]) ).
tcf(c_179,plain,
! [X0: $i] : apply(iPr_def_11,X0) = X0,
inference(superposition,[status(thm)],[c_94,c_172]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i] : apply(apply(apply(s,iPr_def_11),X0),X1) = apply(X1,apply(X0,X1)),
inference(superposition,[status(thm)],[c_179,c_53]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i] : apply(X0,apply(X1,X0)) = apply(apply(iPr_def_12,X1),X0),
inference(light_normalisation,[status(thm)],[c_184,c_95]) ).
tcf(c_214,plain,
! [X0: $i] : apply(X0,apply(iPr_def_11,X0)) = apply(iPr_def_13,X0),
inference(superposition,[status(thm)],[c_96,c_186]) ).
tcf(c_227,plain,
! [X0: $i] : apply(X0,X0) = apply(iPr_def_13,X0),
inference(light_normalisation,[status(thm)],[c_214,c_179]) ).
tcf(c_3219,plain,
! [X0: $i,X1: $i] : apply(apply(apply(iPr_def_14,iPr_def_10),X0),X1) = apply(apply(X0,X1),X1),
inference(superposition,[status(thm)],[c_172,c_165]) ).
tcf(c_3426,plain,
! [X0: $i,X1: $i] : apply(apply(X0,X1),X1) = apply(apply(iPr_def_15,X0),X1),
inference(light_normalisation,[status(thm)],[c_3219,c_98]) ).
tcf(c_3898,plain,
! [X0: $i] : apply(fixed_pt,apply(X0,X0)) = apply(apply(iPr_def_15,iPr_def_17),X0),
inference(superposition,[status(thm)],[c_3426,c_176]) ).
tcf(c_3951,plain,
! [X0: $i] : apply(fixed_pt,apply(X0,X0)) = apply(iPr_def_18,X0),
inference(light_normalisation,[status(thm)],[c_3898,c_101]) ).
tcf(c_4637,plain,
! [X0: $i] : apply(fixed_pt,apply(iPr_def_13,X0)) = apply(iPr_def_18,X0),
inference(superposition,[status(thm)],[c_227,c_3951]) ).
tcf(c_4932,plain,
apply(fixed_pt,iPr_def_19) = apply(iPr_def_18,iPr_def_18),
inference(superposition,[status(thm)],[c_102,c_4637]) ).
tcf(c_4965,plain,
apply(iPr_def_18,iPr_def_18) = iPr_def_20,
inference(light_normalisation,[status(thm)],[c_4932,c_103]) ).
tcf(c_4969,plain,
iPr_def_19 = iPr_def_20,
inference(demodulation,[status(thm)],[c_4965,c_102,c_227]) ).
tcf(c_4973,plain,
iPr_def_19 != iPr_def_19,
inference(demodulation,[status(thm)],[c_104,c_4969]) ).
tcf(c_4974,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_4973]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL006-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n013.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 07:10:22 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 6.03/1.70 % SZS status Started for theBenchmark.p
% 6.03/1.70 % SZS status Unsatisfiable for theBenchmark.p
% 6.03/1.70
% 6.03/1.70 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.03/1.70
% 6.03/1.70 % ------ iProver source info
% 6.03/1.70
% 6.03/1.70 % git: date: 2026-07-19 20:42:38 +0200
% 6.03/1.70 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.03/1.70 % git: non_committed_changes: false
% 6.03/1.70
% 6.03/1.70 % ------ Parsing...% successful
% 6.03/1.70
% 6.03/1.70
% 6.03/1.70 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.03/1.70
% 6.03/1.70 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 1 sf_s rm: 2 0s sf_e pe_s pe_e %
% 6.03/1.70
% 6.03/1.70 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 6.03/1.70 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.03/1.70
% 6.03/1.70 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 6.03/1.70 % ------ Proving...
% 6.03/1.70 % ------ Problem Properties
% 6.03/1.70
% 6.03/1.70 %
% 6.03/1.70 % clauses 14
% 6.03/1.70 % conjectures 0
% 6.03/1.70 % EPR 1
% 6.03/1.70 % Horn 14
% 6.03/1.70 % unary 14
% 6.03/1.70 % binary 0
% 6.03/1.70 % lits 14
% 6.03/1.70 % lits eq 14
% 6.03/1.70 % fd_pure 0
% 6.03/1.70 % fd_pseudo 0
% 6.03/1.70 % fd_cond 0
% 6.03/1.70 % fd_pseudo_cond 0
% 6.03/1.70 % AC symbols 0
% 6.03/1.70
% 6.03/1.70 % ------ Schedule UEQ
% 6.03/1.70
% 6.03/1.70 % ------ Option_UEQ Time Limit: 10.
% 6.03/1.70
% 6.03/1.70
% 6.03/1.70 % ------
% 6.03/1.70 % Current options:
% 6.03/1.70 % ------
% 6.03/1.70
% 6.03/1.70
% 6.03/1.70 %
% 6.03/1.70
% 6.03/1.70 % ------ Proving...
% 6.03/1.70 %
% 6.03/1.70
% 6.03/1.70 % SZS status Unsatisfiable for theBenchmark.p
% 6.03/1.70
% 6.03/1.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.03/1.70
% 6.03/1.70
%------------------------------------------------------------------------------