%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ITP209_3 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n003.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 01:48:29 PM UTC 2026
% Result : Theorem 1.42s 1.32s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 12 equ)
% Maximal formula atoms : 1 ( 4 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 42 ( 42 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 15 !; 0 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
aa_a_fun_a_a: ( a * fun_a_fun_a_a ) > fun_a_a ).
tff(pred_def_1,type,
syntax_ac_operator_a: fun_a_fun_a_a > $o ).
tff(func_def_2,type,
a2: a ).
tff(func_def_3,type,
b: a ).
tff(func_def_4,type,
c: a ).
tff(func_def_5,type,
f: fun_a_fun_a_a ).
tff(func_def_6,type,
sK0: fun_a_fun_a_a > a ).
tff(func_def_7,type,
sK1: fun_a_fun_a_a > a ).
tff(func_def_8,type,
sK2: fun_a_fun_a_a > a ).
tff(func_def_9,type,
sK3: fun_a_fun_a_a > a ).
tff(func_def_10,type,
sK4: fun_a_fun_a_a > a ).
tff(func_def_11,type,
sK5: fun_a_fun_a_a > a ).
tff(func_def_12,type,
sK6: fun_a_fun_a_a > a ).
tff(func_def_13,type,
sK7: fun_a_fun_a_a > a ).
tff(func_def_14,type,
sK8: fun_a_fun_a_a > a ).
tff(func_def_15,type,
sK9: fun_a_fun_a_a > a ).
tff(f2,axiom,
! [X0: a,X1: a] : ( aa_a_a(aa_a_fun_a_a(f,X0),X1) = aa_a_a(aa_a_fun_a_a(f,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_commute) ).
tff(f4,axiom,
! [X0: a,X1: a,X2: a] : ( aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,X0),X1)),X2) = aa_a_a(aa_a_fun_a_a(f,X0),aa_a_a(aa_a_fun_a_a(f,X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_right__assoc) ).
tff(f11,conjecture,
aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) = aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f12,negated_conjecture,
( ( ~ aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) ) = aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
tff(f15,plain,
aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) != aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b),
inference(flattening,[],[f12]) ).
tff(f29,plain,
! [X0: a,X1: a] : ( aa_a_a(aa_a_fun_a_a(f,X0),X1) = aa_a_a(aa_a_fun_a_a(f,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tff(f31,plain,
! [X2: a,X0: a,X1: a] : ( aa_a_a(aa_a_fun_a_a(f,X0),aa_a_a(aa_a_fun_a_a(f,X1),X2)) = aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,X0),X1)),X2) ),
inference(cnf_transformation,[],[f4]) ).
tff(f40,plain,
aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) != aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b),
inference(cnf_transformation,[],[f15]) ).
tcf(c_50,plain,
! [X0_a: a,X1_a: a] : aa_a_a(aa_a_fun_a_a(f,X0_a),X1_a) = aa_a_a(aa_a_fun_a_a(f,X1_a),X0_a),
inference(cnf_transformation,[],[f29]) ).
tcf(c_52,plain,
! [X0_a: a,X1_a: a,X2_a: a] : aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,X0_a),X1_a)),X2_a) = aa_a_a(aa_a_fun_a_a(f,X0_a),aa_a_a(aa_a_fun_a_a(f,X1_a),X2_a)),
inference(cnf_transformation,[],[f31]) ).
tcf(c_61,negated_conjecture,
aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),b)),c) != aa_a_a(aa_a_fun_a_a(f,aa_a_a(aa_a_fun_a_a(f,a2),c)),b),
inference(cnf_transformation,[],[f40]) ).
tcf(c_101,plain,
aa_a_a(aa_a_fun_a_a(f,a2),aa_a_a(aa_a_fun_a_a(f,b),c)) != aa_a_a(aa_a_fun_a_a(f,a2),aa_a_a(aa_a_fun_a_a(f,b),c)),
inference(demodulation,[status(thm)],[c_61,c_50,c_52]) ).
tcf(c_102,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ITP209_3 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.42 % Computer : n003.cluster.edu
% 0.09/0.42 % Model : x86_64 x86_64
% 0.09/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.42 % Memory : 8046.5625MB
% 0.09/0.42 % OS : Linux 6.8.0-71-generic
% 0.09/0.42 % CPULimit : 300
% 0.09/0.42 % WCLimit : 300
% 0.09/0.42 % DateTime : Wed Sep 23 18:04:34 UTC 2026
% 0.09/0.42 % CPUTime :
% 0.09/0.42 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.46 Running first-order theorem proving
% 0.09/0.46 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.47
% 0.13/0.47 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.47
% 0.13/0.47 % Detected problem language: tptp
% 0.13/0.48 % Proving...
% 1.42/1.32 % SZS status Started for theBenchmark.p
% 1.42/1.32 % SZS status Theorem for theBenchmark.p
% 1.42/1.32
% 1.42/1.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.42/1.32
% 1.42/1.32 % ------ iProver source info
% 1.42/1.32
% 1.42/1.32 % git: date: 2026-07-19 20:42:38 +0200
% 1.42/1.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.42/1.32 % git: non_committed_changes: false
% 1.42/1.32
% 1.42/1.32 % ------ Parsing...
% 1.42/1.32 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Global Options Modified: tff_prep: switching off prep_sem_filter, sub_typing, pure_diseq_elim
% 1.42/1.32 %
% 1.42/1.32
% 1.42/1.32 % ------ Preprocessing...%
% 1.42/1.32
% 1.42/1.32 % SZS status Theorem for theBenchmark.p
% 1.42/1.32
% 1.42/1.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.42/1.32
% 1.42/1.32
%------------------------------------------------------------------------------