%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP125-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n005.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 01:31:12 PM UTC 2026
% Result : Unsatisfiable 1.85s 1.23s
% Output : CNFRefutation 1.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of formulae : 37 ( 11 unt; 0 def)
% Number of atoms : 98 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 115 ( 54 ~; 61 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 55 ( 0 sgn 55 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( product(e_3,X0,X1)
| product(e_2,X0,X1)
| product(e_1,X0,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',row_surjectivity) ).
fof(f4,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ product(X1,X0,X3)
| ~ product(X3,X2,X1)
| product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3_2) ).
fof(f5,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f6,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f8,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f14,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(f15,axiom,
! [X2,X3,X0,X1] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function2) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f17,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(f18,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).
tcf(c_69,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X1,X0,X3)
| ~ product(X2,X3,X0)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_71,plain,
! [X0: $i] : product(X0,X0,X0),
inference(cnf_transformation,[],[f18]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f16]) ).
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,[],[f15]) ).
tcf(c_80,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[],[f8]) ).
tcf(c_81,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,[],[f14]) ).
tcf(c_82,plain,
group_element(e_2),
inference(cnf_transformation,[],[f6]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( product(e_3,X0,X1)
| product(e_2,X0,X1)
| product(e_1,X0,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_86,plain,
group_element(e_1),
inference(cnf_transformation,[],[f5]) ).
tcf(c_87,plain,
product(e_1,e_1,e_1),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[c_80,c_74]) ).
tcf(c_176,plain,
( ~ product(e_1,e_1,e_2)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_175]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_80,c_73]) ).
tcf(c_184,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_183]) ).
tcf(c_191,plain,
! [X0: $i,X1: $i] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_80,c_72]) ).
tcf(c_192,plain,
( ~ product(e_2,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_191]) ).
tcf(c_279,plain,
product(e_2,e_2,e_2),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_282,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,e_2,X1)
| ~ product(e_2,X2,X0)
| ~ product(X0,X1,e_2) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_331,plain,
! [X0: $i] :
( product(e_2,X0,e_3)
| product(e_2,X0,e_2)
| product(e_2,X0,e_1)
| ~ group_element(e_2)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_81]) ).
tcf(c_333,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| ~ group_element(e_2)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_331]) ).
tcf(c_366,plain,
! [X0: $i] :
( product(e_3,X0,e_2)
| product(e_2,X0,e_2)
| product(e_1,X0,e_2)
| ~ group_element(e_2)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_84]) ).
tcf(c_368,plain,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_2)
| ~ group_element(e_2)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_366]) ).
tcf(c_428,plain,
( ~ product(e_2,e_2,e_2)
| ~ product(e_2,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_183]) ).
tcf(c_691,plain,
! [X0: $i,X1: $i] :
( product(X0,e_2,X1)
| ~ product(e_3,X1,e_2)
| ~ product(e_2,X0,e_3) ),
inference(instantiation,[status(thm)],[c_282]) ).
tcf(c_692,plain,
( product(e_1,e_2,e_1)
| ~ product(e_3,e_1,e_2)
| ~ product(e_2,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_691]) ).
tcf(c_693,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_692,c_428,c_368,c_333,c_279,c_192,c_184,c_176,c_87,c_82,c_86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP125-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n005.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Wed Sep 23 13:40:17 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running EPR theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 1.85/1.23 % SZS status Started for theBenchmark.p
% 1.85/1.23 % SZS status Unsatisfiable for theBenchmark.p
% 1.85/1.23
% 1.85/1.23 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.85/1.23
% 1.85/1.23 % ------ iProver source info
% 1.85/1.23
% 1.85/1.23 % git: date: 2026-07-19 20:42:38 +0200
% 1.85/1.23 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.85/1.23 % git: non_committed_changes: false
% 1.85/1.23
% 1.85/1.23 % ------ Parsing...% successful
% 1.85/1.23
% 1.85/1.23
% 1.85/1.23 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 1.85/1.23 %
% 1.85/1.23
% 1.85/1.23 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e %
% 1.85/1.23
% 1.85/1.23 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 1.85/1.23 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.85/1.23 % ------ Proving...
% 1.85/1.23 % ------ Problem Properties
% 1.85/1.23
% 1.85/1.23 %
% 1.85/1.23 % clauses 19
% 1.85/1.23 % conjectures 3
% 1.85/1.23 % EPR 19
% 1.85/1.23 % Horn 16
% 1.85/1.23 % unary 4
% 1.85/1.23 % binary 9
% 1.85/1.23 % lits 46
% 1.85/1.23 % lits eq 0
% 1.85/1.23 % fd_pure 0
% 1.85/1.23 % fd_pseudo 0
% 1.85/1.23 % fd_cond 0
% 1.85/1.23 % fd_pseudo_cond 0
% 1.85/1.23 % AC symbols 0
% 1.85/1.23
% 1.85/1.23 % ------ Schedule EPR non Horn non eq is on
% 1.85/1.23
% 1.85/1.23 % ------ no equalities: superposition off
% 1.85/1.23
% 1.85/1.23 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 1.85/1.23
% 1.85/1.23
% 1.85/1.23 % ------
% 1.85/1.23 % Current options:
% 1.85/1.23 % ------
% 1.85/1.23
% 1.85/1.23
% 1.85/1.23 %
% 1.85/1.23
% 1.85/1.23 % ------ Proving...
% 1.85/1.23 %
% 1.85/1.23
% 1.85/1.23 % SZS status Unsatisfiable for theBenchmark.p
% 1.85/1.23
% 1.85/1.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.85/1.23
% 1.85/1.23
%------------------------------------------------------------------------------