%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL003-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 01:02:28 PM UTC 2026
% Result : Unsatisfiable 10.25s 2.11s
% Output : CNFRefutation 10.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 49 ( 49 unt; 9 def)
% Number of atoms : 104 ( 48 equ)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 5 ( 5 ~; 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 : 11 ( 9 usr; 10 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 58 ( 0 sgn 58 !; 0 ?; 48 :)
% 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,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_definition) ).
fof(f3,axiom,
! [X0,X1] : apply(apply(w,X0),X1) = apply(apply(X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_definition) ).
fof(f4,axiom,
! [X0] : ifeq(apply(X0,fixed_pt),apply(fixed_pt,apply(X0,fixed_pt)),fixed_point(X0),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f5,plain,
! [X0] : true = ifeq(apply(X0,fixed_pt),apply(fixed_pt,apply(X0,fixed_pt)),fixed_point(X0),true),
inference(reorient_equations,[],[f4]) ).
fof(f6,negated_conjecture,
fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b)) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
fof(f7,plain,
true != fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b)),
inference(reorient_equations,[],[f6]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[],[f1]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : apply(apply(X0,X1),X1) = apply(apply(w,X0),X1),
inference(cnf_transformation,[],[f3]) ).
tcf(c_57,plain,
! [X0: $i] : ifeq(apply(X0,fixed_pt),apply(fixed_pt,apply(X0,fixed_pt)),fixed_point(X0),true) = true,
inference(cnf_transformation,[],[f5]) ).
tcf(c_58,negated_conjecture,
fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b)) != true,
inference(cnf_transformation,[],[f7]) ).
tcf(c_78,definition,
iPr_def_10 = apply(w,w),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_79,definition,
iPr_def_11 = apply(b,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_80,definition,
iPr_def_12 = apply(b,w),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_81,definition,
iPr_def_13 = apply(b,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_82,definition,
iPr_def_14 = apply(iPr_def_13,b),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_83,definition,
iPr_def_15 = apply(iPr_def_11,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_84,definition,
iPr_def_16 = apply(b,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_85,definition,
iPr_def_17 = apply(iPr_def_16,b),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_86,definition,
iPr_def_18 = fixed_point(iPr_def_17),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_87,negated_conjecture,
iPr_def_18 != true,
inference(demodulation,[status(thm)],[c_58,c_80,c_81,c_82,c_78,c_79,c_83,c_84,c_85,c_86]) ).
tcf(c_88,plain,
! [X0: $i] : ifeq(apply(X0,fixed_pt),apply(fixed_pt,apply(X0,fixed_pt)),fixed_point(X0),true) = true,
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] : apply(apply(X0,X1),X1) = apply(apply(w,X0),X1),
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] : ifeq(X0,X0,X1,X2) = X1,
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_157,plain,
ifeq(apply(iPr_def_17,fixed_pt),apply(fixed_pt,apply(iPr_def_17,fixed_pt)),iPr_def_18,true) = true,
inference(superposition,[status(thm)],[c_86,c_88]) ).
tcf(c_166,plain,
! [X0: $i] : apply(apply(w,X0),X0) = apply(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_78,c_89]) ).
tcf(c_171,plain,
! [X0: $i] : apply(apply(X0,X0),X0) = apply(apply(w,w),X0),
inference(superposition,[status(thm)],[c_89,c_89]) ).
tcf(c_173,plain,
! [X0: $i] : apply(apply(X0,X0),X0) = apply(iPr_def_10,X0),
inference(demodulation,[status(thm)],[c_171,c_78]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_12,X0),X1) = apply(w,apply(X0,X1)),
inference(superposition,[status(thm)],[c_80,c_90]) ).
tcf(c_187,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_11,X0),X1) = apply(iPr_def_10,apply(X0,X1)),
inference(superposition,[status(thm)],[c_79,c_90]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_13,X0),X1) = apply(iPr_def_12,apply(X0,X1)),
inference(superposition,[status(thm)],[c_81,c_90]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i] : apply(apply(iPr_def_16,X0),X1) = apply(iPr_def_15,apply(X0,X1)),
inference(superposition,[status(thm)],[c_84,c_90]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(w,apply(apply(b,X0),X1)),X2) = apply(apply(X0,apply(X1,X2)),X2),
inference(superposition,[status(thm)],[c_90,c_89]) ).
tcf(c_310,plain,
! [X0: $i] : apply(iPr_def_10,apply(iPr_def_14,X0)) = apply(iPr_def_15,X0),
inference(superposition,[status(thm)],[c_83,c_187]) ).
tcf(c_330,plain,
! [X0: $i] : apply(iPr_def_12,apply(b,X0)) = apply(iPr_def_14,X0),
inference(superposition,[status(thm)],[c_82,c_188]) ).
tcf(c_364,plain,
! [X0: $i,X1: $i] : apply(w,apply(apply(b,X0),X1)) = apply(apply(iPr_def_14,X0),X1),
inference(superposition,[status(thm)],[c_330,c_186]) ).
tcf(c_553,plain,
! [X0: $i] : apply(iPr_def_15,apply(b,X0)) = apply(iPr_def_17,X0),
inference(superposition,[status(thm)],[c_85,c_189]) ).
tcf(c_623,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(X0,apply(X1,X2)),X2) = apply(apply(apply(iPr_def_14,X0),X1),X2),
inference(light_normalisation,[status(thm)],[c_190,c_364]) ).
tcf(c_692,plain,
! [X0: $i,X1: $i] : apply(apply(X0,apply(X1,X1)),X1) = apply(apply(w,apply(iPr_def_14,X0)),X1),
inference(superposition,[status(thm)],[c_623,c_89]) ).
tcf(c_5154,plain,
! [X0: $i,X1: $i] : apply(apply(w,apply(iPr_def_14,apply(b,X0))),X1) = apply(X0,apply(apply(X1,X1),X1)),
inference(superposition,[status(thm)],[c_692,c_90]) ).
tcf(c_5234,plain,
! [X0: $i,X1: $i] : apply(apply(w,apply(iPr_def_14,apply(b,X0))),X1) = apply(X0,apply(iPr_def_10,X1)),
inference(demodulation,[status(thm)],[c_5154,c_173]) ).
tcf(c_8696,plain,
! [X0: $i] : apply(X0,apply(iPr_def_10,apply(iPr_def_14,apply(b,X0)))) = apply(iPr_def_10,apply(iPr_def_14,apply(b,X0))),
inference(superposition,[status(thm)],[c_5234,c_166]) ).
tcf(c_8727,plain,
! [X0: $i] : apply(X0,apply(iPr_def_17,X0)) = apply(iPr_def_17,X0),
inference(demodulation,[status(thm)],[c_8696,c_310,c_553]) ).
tcf(c_8764,plain,
ifeq(apply(iPr_def_17,fixed_pt),apply(iPr_def_17,fixed_pt),iPr_def_18,true) = true,
inference(demodulation,[status(thm)],[c_157,c_8727]) ).
tcf(c_8765,plain,
true = iPr_def_18,
inference(demodulation,[status(thm)],[c_8764,c_91]) ).
tcf(c_8788,plain,
iPr_def_18 != iPr_def_18,
inference(demodulation,[status(thm)],[c_87,c_8765]) ).
tcf(c_8789,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_8788]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL003-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 07:08:14 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.40 Running UEQ theorem proving
% 0.08/0.40 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
% 0.08/0.41
% 0.08/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.41
% 0.08/0.41 % Detected problem language: tptp
% 0.08/0.42 % Proving...
% 10.25/2.11 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 10.25/2.11 % SZS status Started for theBenchmark.p
% 10.25/2.11 % SZS status Unsatisfiable for theBenchmark.p
% 10.25/2.11
% 10.25/2.11 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.25/2.11
% 10.25/2.11 % ------ iProver source info
% 10.25/2.11
% 10.25/2.11 % git: date: 2026-07-19 20:42:38 +0200
% 10.25/2.11 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.25/2.11 % git: non_committed_changes: false
% 10.25/2.11
% 10.25/2.11 % ------ Parsing...% successful
% 10.25/2.11
% 10.25/2.11
% 10.25/2.11 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.25/2.11
% 10.25/2.11 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 10.25/2.11
% 10.25/2.11 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.25/2.11
% 10.25/2.11 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 10.25/2.11 % ------ Proving...
% 10.25/2.11 % ------ Problem Properties
% 10.25/2.11
% 10.25/2.11 %
% 10.25/2.11 % clauses 14
% 10.25/2.11 % conjectures 1
% 10.25/2.11 % EPR 1
% 10.25/2.11 % Horn 14
% 10.25/2.11 % unary 14
% 10.25/2.11 % binary 0
% 10.25/2.11 % lits 14
% 10.25/2.11 % lits eq 14
% 10.25/2.11 % fd_pure 0
% 10.25/2.11 % fd_pseudo 0
% 10.25/2.11 % fd_cond 0
% 10.25/2.11 % fd_pseudo_cond 0
% 10.25/2.11 % AC symbols 0
% 10.25/2.11
% 10.25/2.11 % ------ Input Options Time Limit: Unbounded
% 10.25/2.11
% 10.25/2.11
% 10.25/2.11 % ------
% 10.25/2.11 % Current options:
% 10.25/2.11 % ------
% 10.25/2.11
% 10.25/2.11
% 10.25/2.11 %
% 10.25/2.11
% 10.25/2.11 % ------ Proving...
% 10.25/2.11 %
% 10.25/2.11
% 10.25/2.11 % SZS status Unsatisfiable for theBenchmark.p
% 10.25/2.11
% 10.25/2.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.25/2.11
% 10.25/2.11
%------------------------------------------------------------------------------