%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : COL063-1 : 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 : n002.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 01:02:43 PM UTC 2026
% Result : Unsatisfiable 8.89s 7.11s
% Output : CNFRefutation 8.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 15 unt; 0 def)
% Number of atoms : 15 ( 14 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 32 !; 0 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
fof(f2,axiom,
! [X0,X1] : apply(apply(t,X0),X1) = apply(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t_definition) ).
fof(f3,negated_conjecture,
! [X0] : apply(apply(apply(X0,f(X0)),g(X0)),h(X0)) != apply(apply(h(X0),g(X0)),f(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_f_combinator) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(cnf_transformation,[],[f1]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] : apply(apply(t,X0),X1) = apply(X1,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_54,negated_conjecture,
! [X0: $i] : apply(apply(apply(X0,f(X0)),g(X0)),h(X0)) != apply(apply(h(X0),g(X0)),f(X0)),
inference(cnf_transformation,[],[f3]) ).
tcf(c_67,negated_conjecture,
! [X0: $i] : apply(apply(apply(X0,f(X0)),g(X0)),h(X0)) != apply(apply(h(X0),g(X0)),f(X0)),
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_2876,plain,
! [X0: $i,X1: $i] : apply(apply(apply(X0,apply(X1,f(apply(apply(b,X0),X1)))),g(apply(apply(b,X0),X1))),h(apply(apply(b,X0),X1))) != apply(apply(h(apply(apply(b,X0),X1)),g(apply(apply(b,X0),X1))),f(apply(apply(b,X0),X1))),
inference(superposition,[status(thm)],[c_52,c_67]) ).
tcf(c_2881,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(X0,apply(X1,apply(X2,f(apply(apply(b,apply(apply(b,X0),X1)),X2))))),g(apply(apply(b,apply(apply(b,X0),X1)),X2))),h(apply(apply(b,apply(apply(b,X0),X1)),X2))) != apply(apply(h(apply(apply(b,apply(apply(b,X0),X1)),X2)),g(apply(apply(b,apply(apply(b,X0),X1)),X2))),f(apply(apply(b,apply(apply(b,X0),X1)),X2))),
inference(superposition,[status(thm)],[c_52,c_2876]) ).
tcf(c_2892,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : apply(apply(apply(X0,apply(X1,apply(X2,apply(X3,f(apply(apply(b,apply(apply(b,X0),X1)),apply(apply(b,X2),X3))))))),g(apply(apply(b,apply(apply(b,X0),X1)),apply(apply(b,X2),X3)))),h(apply(apply(b,apply(apply(b,X0),X1)),apply(apply(b,X2),X3)))) != apply(apply(h(apply(apply(b,apply(apply(b,X0),X1)),apply(apply(b,X2),X3))),g(apply(apply(b,apply(apply(b,X0),X1)),apply(apply(b,X2),X3)))),f(apply(apply(b,apply(apply(b,X0),X1)),apply(apply(b,X2),X3)))),
inference(superposition,[status(thm)],[c_52,c_2881]) ).
tcf(c_2926,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : apply(apply(apply(apply(X0,apply(X1,apply(X2,f(apply(apply(b,apply(apply(b,apply(t,X3)),X0)),apply(apply(b,X1),X2)))))),X3),g(apply(apply(b,apply(apply(b,apply(t,X3)),X0)),apply(apply(b,X1),X2)))),h(apply(apply(b,apply(apply(b,apply(t,X3)),X0)),apply(apply(b,X1),X2)))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X3)),X0)),apply(apply(b,X1),X2))),g(apply(apply(b,apply(apply(b,apply(t,X3)),X0)),apply(apply(b,X1),X2)))),f(apply(apply(b,apply(apply(b,apply(t,X3)),X0)),apply(apply(b,X1),X2)))),
inference(superposition,[status(thm)],[c_53,c_2892]) ).
tcf(c_3874,plain,
! [X0: $i,X1: $i,X2: $i] : apply(apply(apply(X0,apply(X1,f(apply(apply(b,apply(apply(b,apply(t,X2)),b)),apply(apply(b,X0),X1))))),apply(X2,g(apply(apply(b,apply(apply(b,apply(t,X2)),b)),apply(apply(b,X0),X1))))),h(apply(apply(b,apply(apply(b,apply(t,X2)),b)),apply(apply(b,X0),X1)))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X2)),b)),apply(apply(b,X0),X1))),g(apply(apply(b,apply(apply(b,apply(t,X2)),b)),apply(apply(b,X0),X1)))),f(apply(apply(b,apply(apply(b,apply(t,X2)),b)),apply(apply(b,X0),X1)))),
inference(superposition,[status(thm)],[c_52,c_2926]) ).
tcf(c_3887,plain,
! [X0: $i,X1: $i] : apply(apply(X0,f(apply(apply(b,apply(apply(b,apply(t,X1)),b)),apply(apply(b,b),X0)))),apply(apply(X1,g(apply(apply(b,apply(apply(b,apply(t,X1)),b)),apply(apply(b,b),X0)))),h(apply(apply(b,apply(apply(b,apply(t,X1)),b)),apply(apply(b,b),X0))))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X1)),b)),apply(apply(b,b),X0))),g(apply(apply(b,apply(apply(b,apply(t,X1)),b)),apply(apply(b,b),X0)))),f(apply(apply(b,apply(apply(b,apply(t,X1)),b)),apply(apply(b,b),X0)))),
inference(superposition,[status(thm)],[c_52,c_3874]) ).
tcf(c_5272,plain,
! [X0: $i] : apply(apply(apply(X0,g(apply(apply(b,apply(apply(b,apply(t,X0)),b)),apply(apply(b,b),t)))),h(apply(apply(b,apply(apply(b,apply(t,X0)),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,X0)),b)),apply(apply(b,b),t)))) != apply(apply(h(apply(apply(b,apply(apply(b,apply(t,X0)),b)),apply(apply(b,b),t))),g(apply(apply(b,apply(apply(b,apply(t,X0)),b)),apply(apply(b,b),t)))),f(apply(apply(b,apply(apply(b,apply(t,X0)),b)),apply(apply(b,b),t)))),
inference(superposition,[status(thm)],[c_53,c_3887]) ).
tcf(c_5309,plain,
$false,
inference(superposition,[status(thm)],[c_53,c_5272]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL063-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.38 % Computer : n002.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.39 % CPULimit : 300
% 0.10/5.39 % WCLimit : 300
% 0.10/5.39 % DateTime : Fri Sep 25 07:27:27 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.42 Running UEQ theorem proving
% 0.15/5.42 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
% 0.15/5.43
% 0.15/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.43
% 0.15/5.44 % Detected problem language: tptp
% 0.15/5.45 % Proving...
% 8.89/7.11 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 8.89/7.11 % SZS status Started for theBenchmark.p
% 8.89/7.11 % SZS status Unsatisfiable for theBenchmark.p
% 8.89/7.11
% 8.89/7.11 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.89/7.11
% 8.89/7.11 % ------ iProver source info
% 8.89/7.11
% 8.89/7.11 % git: date: 2026-07-19 20:42:38 +0200
% 8.89/7.11 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.89/7.11 % git: non_committed_changes: false
% 8.89/7.11
% 8.89/7.11 % ------ Parsing...% successful
% 8.89/7.11
% 8.89/7.11
% 8.89/7.11 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.89/7.11
% 8.89/7.11 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 8.89/7.11
% 8.89/7.11 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.89/7.11
% 8.89/7.11 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 8.89/7.11 % ------ Proving...
% 8.89/7.11 % ------ Problem Properties
% 8.89/7.11
% 8.89/7.11 %
% 8.89/7.11 % clauses 3
% 8.89/7.11 % conjectures 1
% 8.89/7.11 % EPR 0
% 8.89/7.11 % Horn 3
% 8.89/7.11 % unary 3
% 8.89/7.11 % binary 0
% 8.89/7.11 % lits 3
% 8.89/7.11 % lits eq 3
% 8.89/7.11 % fd_pure 0
% 8.89/7.11 % fd_pseudo 0
% 8.89/7.11 % fd_cond 0
% 8.89/7.11 % fd_pseudo_cond 0
% 8.89/7.11 % AC symbols 0
% 8.89/7.11
% 8.89/7.11 % ------ Input Options Time Limit: Unbounded
% 8.89/7.11
% 8.89/7.11
% 8.89/7.11 % ------
% 8.89/7.11 % Current options:
% 8.89/7.11 % ------
% 8.89/7.11
% 8.89/7.11
% 8.89/7.11 %
% 8.89/7.11
% 8.89/7.11 % ------ Proving...
% 8.89/7.11 %
% 8.89/7.11
% 8.89/7.11 % SZS status Unsatisfiable for theBenchmark.p
% 8.89/7.11
% 8.89/7.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.89/7.11
% 8.89/7.11
%------------------------------------------------------------------------------