%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP125-1.003 : TPTP v9.3.1. Released v1.2.0.
% 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 01:31:11 PM UTC 2026
% Result : Unsatisfiable 0.99s 1.17s
% Output : CNFRefutation 0.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 14 unt; 0 def)
% Number of atoms : 96 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 112 ( 56 ~; 56 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 52 ( 0 sgn 52 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f4,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f5,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f10,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/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
fof(f11,axiom,
! [X2,X3,X0,X1] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).
fof(f12,axiom,
! [X2,X3,X0,X1] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f13,axiom,
! [X2,X3,X0,X1] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f14,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
fof(f15,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X2,X3,X0)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).
tcf(c_64,plain,
group_element(e_1),
inference(cnf_transformation,[],[f1]) ).
tcf(c_66,plain,
group_element(e_3),
inference(cnf_transformation,[],[f3]) ).
tcf(c_67,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[],[f4]) ).
tcf(c_68,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[],[f5]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_77,plain,
! [X0: $i] : product(X0,X0,X0),
inference(cnf_transformation,[],[f14]) ).
tcf(c_78,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X2,X3,X0)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_79,plain,
product(e_1,e_1,e_1),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_135,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[c_67,c_74]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_68,c_75]) ).
tcf(c_168,plain,
( ~ product(e_1,e_3,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_167]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_68,c_76]) ).
tcf(c_176,plain,
( ~ product(e_3,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_175]) ).
tcf(c_234,plain,
( ~ product(e_2,e_2,e_2)
| ~ product(e_2,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_135]) ).
tcf(c_235,plain,
product(e_2,e_2,e_2),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_243,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_2,X2,X1)
| ~ product(X1,X0,e_2)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_78]) ).
tcf(c_245,plain,
product(e_3,e_3,e_3),
inference(instantiation,[status(thm)],[c_77]) ).
tcf(c_269,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_73]) ).
tcf(c_272,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_269]) ).
tcf(c_273,plain,
! [X0: $i] :
( product(e_3,X0,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_276,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| ~ group_element(e_3)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_273]) ).
tcf(c_312,plain,
( ~ product(e_3,e_3,e_3)
| ~ product(e_3,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_167]) ).
tcf(c_314,plain,
( ~ product(e_3,e_3,e_3)
| ~ product(e_1,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_175]) ).
tcf(c_362,plain,
! [X0: $i,X1: $i] :
( product(e_2,X1,X0)
| ~ product(X0,e_3,e_2)
| ~ product(e_3,X0,X1) ),
inference(instantiation,[status(thm)],[c_243]) ).
tcf(c_461,plain,
! [X0: $i] :
( product(e_2,e_2,X0)
| ~ product(e_3,X0,e_2)
| ~ product(X0,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_362]) ).
tcf(c_462,plain,
( product(e_2,e_2,e_1)
| ~ product(e_3,e_1,e_2)
| ~ product(e_1,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_461]) ).
tcf(c_463,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_462,c_314,c_312,c_276,c_272,c_245,c_235,c_234,c_176,c_168,c_79,c_64,c_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP125-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.39 % Computer : n002.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Wed Sep 23 13:42:33 UTC 2026
% 0.02/0.40 % CPUTime :
% 0.02/0.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.02/0.45 Running EPR theorem proving
% 0.02/0.45 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s epr_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.48
% 0.21/0.48 % ======== iProver multi-core TPTP/SMT =========
% 0.21/0.48
% 0.21/0.48 % Detected problem language: tptp
% 0.21/0.49 % Proving...
% 0.99/1.17 % SZS status Started for theBenchmark.p
% 0.99/1.17 % SZS status Unsatisfiable for theBenchmark.p
% 0.99/1.17
% 0.99/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.99/1.17
% 0.99/1.17 % ------ iProver source info
% 0.99/1.17
% 0.99/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 0.99/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.99/1.17 % git: non_committed_changes: false
% 0.99/1.17
% 0.99/1.17 % ------ Parsing...% successful
% 0.99/1.17
% 0.99/1.17
% 0.99/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 0.99/1.17 %
% 0.99/1.17
% 0.99/1.17 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e %
% 0.99/1.17
% 0.99/1.17 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 0.99/1.17 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.99/1.17 % ------ Proving...
% 0.99/1.17 % ------ Problem Properties
% 0.99/1.17
% 0.99/1.17 %
% 0.99/1.17 % clauses 15
% 0.99/1.17 % conjectures 1
% 0.99/1.17 % EPR 15
% 0.99/1.17 % Horn 14
% 0.99/1.17 % unary 4
% 0.99/1.17 % binary 9
% 0.99/1.17 % lits 30
% 0.99/1.17 % lits eq 0
% 0.99/1.17 % fd_pure 0
% 0.99/1.17 % fd_pseudo 0
% 0.99/1.17 % fd_cond 0
% 0.99/1.17 % fd_pseudo_cond 0
% 0.99/1.17 % AC symbols 0
% 0.99/1.17
% 0.99/1.17 % ------ Schedule EPR non Horn non eq is on
% 0.99/1.17
% 0.99/1.17 % ------ no equalities: superposition off
% 0.99/1.17
% 0.99/1.17 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 0.99/1.17
% 0.99/1.17
% 0.99/1.17 % ------
% 0.99/1.17 % Current options:
% 0.99/1.17 % ------
% 0.99/1.17
% 0.99/1.17
% 0.99/1.17 %
% 0.99/1.17
% 0.99/1.17 % ------ Proving...
% 0.99/1.17 %
% 0.99/1.17
% 0.99/1.17 % SZS status Unsatisfiable for theBenchmark.p
% 0.99/1.17
% 0.99/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.99/1.17
% 0.99/1.17
%------------------------------------------------------------------------------