%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP123-3.003 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n011.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 01:31:07 PM UTC 2026
% Result : Unsatisfiable 0.85s 1.10s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 12
% Syntax : Number of formulae : 41 ( 19 unt; 0 def)
% Number of atoms : 108 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 134 ( 67 ~; 67 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 56 ( 0 sgn 56 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f18,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f19,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f20,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f21,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f22,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f23,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f26,axiom,
! [X0,X1] :
( product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).
fof(f29,axiom,
! [X2,X3,X0,X1] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f30,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
fof(f31,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( equalish(X0,X3)
| ~ product(X5,X4,X3)
| ~ product(X5,X1,X0)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1_1) ).
fof(f32,negated_conjecture,
! [X2,X3,X0,X1,X4,X5] :
( equalish(X1,X4)
| ~ product(X5,X4,X3)
| ~ product(X5,X1,X0)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg1_2) ).
tcf(c_97,plain,
group_element(e_1),
inference(cnf_transformation,[],[f17]) ).
tcf(c_98,plain,
group_element(e_2),
inference(cnf_transformation,[],[f18]) ).
tcf(c_99,plain,
group_element(e_3),
inference(cnf_transformation,[],[f19]) ).
tcf(c_100,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[],[f20]) ).
tcf(c_101,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[],[f21]) ).
tcf(c_102,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[],[f22]) ).
tcf(c_103,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[],[f23]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] :
( product(X1,X0,e_3)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_110,plain,
! [X0: $i] : product(X0,X0,X0),
inference(cnf_transformation,[],[f30]) ).
tcf(c_111,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( equalish(X0,X3)
| ~ product(X5,X4,X3)
| ~ product(X5,X1,X0)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_112,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( equalish(X1,X4)
| ~ product(X5,X4,X3)
| ~ product(X5,X1,X0)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_113,plain,
product(e_1,e_1,e_1),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_386,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ product(X3,e_1,X1)
| ~ product(X2,e_3,X0)
| ~ product(X2,e_1,X3)
| ~ product(X0,e_3,X1) ),
inference(resolution,[status(thm)],[c_112,c_101]) ).
tcf(c_387,plain,
( ~ product(e_1,e_3,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_386]) ).
tcf(c_734,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(e_2,e_1)
| ~ product(e_2,X1,X3)
| ~ product(e_1,X2,X3)
| ~ product(X0,X2,e_1)
| ~ product(X0,X1,e_2) ),
inference(instantiation,[status(thm)],[c_111]) ).
tcf(c_753,plain,
! [X0: $i,X1: $i] :
( equalish(e_1,e_2)
| ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_754,plain,
! [X0: $i,X1: $i] :
( equalish(e_1,e_3)
| ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_756,plain,
! [X0: $i,X1: $i] :
( equalish(e_2,e_3)
| ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_788,plain,
product(e_3,e_3,e_3),
inference(instantiation,[status(thm)],[c_110]) ).
tcf(c_790,plain,
! [X0: $i] :
( product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_106]) ).
tcf(c_791,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_790]) ).
tcf(c_919,plain,
( equalish(e_2,e_3)
| ~ product(e_3,e_3,e_3)
| ~ product(e_2,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_756]) ).
tcf(c_920,plain,
( equalish(e_1,e_3)
| ~ product(e_3,e_3,e_3)
| ~ product(e_1,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_754]) ).
tcf(c_966,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(e_2,e_1)
| ~ product(e_2,e_3,X2)
| ~ product(X0,e_3,e_2)
| ~ product(e_1,X1,X2)
| ~ product(X0,X1,e_1) ),
inference(instantiation,[status(thm)],[c_734]) ).
tcf(c_967,plain,
( equalish(e_2,e_1)
| ~ product(e_2,e_3,e_1)
| ~ product(e_1,e_3,e_2)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_966]) ).
tcf(c_970,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_2) ),
inference(instantiation,[status(thm)],[c_790]) ).
tcf(c_972,plain,
( equalish(e_1,e_2)
| ~ product(e_2,e_3,e_2)
| ~ product(e_1,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_753]) ).
tcf(c_973,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_972,c_970,c_967,c_919,c_920,c_791,c_788,c_387,c_100,c_101,c_102,c_103,c_113,c_97,c_98,c_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP123-3.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n011.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 : Wed Sep 23 13:35:57 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running EPR theorem proving
% 0.12/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s epr_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 0.85/1.10 % SZS status Started for theBenchmark.p
% 0.85/1.10 % SZS status Unsatisfiable for theBenchmark.p
% 0.85/1.10
% 0.85/1.10 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.85/1.10
% 0.85/1.10 % ------ iProver source info
% 0.85/1.10
% 0.85/1.10 % git: date: 2026-07-19 20:42:38 +0200
% 0.85/1.10 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.85/1.10 % git: non_committed_changes: false
% 0.85/1.10
% 0.85/1.10 % ------ Parsing...% successful
% 0.85/1.10
% 0.85/1.10
% 0.85/1.10 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 0.85/1.10 %
% 0.85/1.10
% 0.85/1.10 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.85/1.10
% 0.85/1.10 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 0.85/1.10 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.85/1.10 % ------ Proving...
% 0.85/1.10 % ------ Problem Properties
% 0.85/1.10
% 0.85/1.10 %
% 0.85/1.10 % clauses 32
% 0.85/1.10 % conjectures 2
% 0.85/1.10 % EPR 32
% 0.85/1.10 % Horn 30
% 0.85/1.10 % unary 20
% 0.85/1.10 % binary 0
% 0.85/1.10 % lits 71
% 0.85/1.10 % lits eq 0
% 0.85/1.10 % fd_pure 0
% 0.85/1.10 % fd_pseudo 0
% 0.85/1.10 % fd_cond 0
% 0.85/1.10 % fd_pseudo_cond 0
% 0.85/1.10 % AC symbols 0
% 0.85/1.10
% 0.85/1.10 % ------ Schedule EPR non Horn non eq is on
% 0.85/1.10
% 0.85/1.10 % ------ no equalities: superposition off
% 0.85/1.10
% 0.85/1.10 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 0.85/1.10
% 0.85/1.10
% 0.85/1.10 % ------
% 0.85/1.10 % Current options:
% 0.85/1.10 % ------
% 0.85/1.10
% 0.85/1.10
% 0.85/1.10 %
% 0.85/1.10
% 0.85/1.10 % ------ Proving...
% 0.85/1.10 %
% 0.85/1.10
% 0.85/1.10 % SZS status Unsatisfiable for theBenchmark.p
% 0.85/1.10
% 0.85/1.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.85/1.10
% 0.85/1.10
%------------------------------------------------------------------------------