%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP131-1.002 : 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 : n018.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 01:31:30 PM UTC 2026
% Result : Unsatisfiable 1.68s 1.21s
% Output : CNFRefutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 9 unt; 0 def)
% Number of atoms : 147 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 196 ( 93 ~; 103 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 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 : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 78 ( 0 sgn 78 !; 0 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f3,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f4,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
fof(f5,axiom,
! [X0,X1] :
( 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(f7,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(f8,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(f9,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/sandbox2/benchmark/theBenchmark.p',qg1_1) ).
fof(f10,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/sandbox2/benchmark/theBenchmark.p',qg1_2) ).
tcf(c_59,plain,
group_element(e_1),
inference(cnf_transformation,[],[f1]) ).
tcf(c_60,plain,
group_element(e_2),
inference(cnf_transformation,[],[f2]) ).
tcf(c_61,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[],[f3]) ).
tcf(c_62,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[],[f4]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_67,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,[],[f9]) ).
tcf(c_68,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,[],[f10]) ).
tcf(c_70,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X2,X1)
| product(X0,X2,e_1)
| ~ group_element(X2)
| ~ group_element(X0)
| ~ product(X0,X1,e_2) ),
inference(superposition,[status(thm)],[c_63,c_65]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X2,X0)
| product(X1,X2,e_1)
| product(X1,X0,e_1)
| ~ group_element(X2)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_63,c_86]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(e_1,e_2)
| ~ product(e_2,X2,X3)
| ~ product(e_1,X1,X3)
| ~ product(X0,X2,e_2)
| ~ product(X0,X1,e_1) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(e_1,e_2)
| ~ product(X3,e_2,X2)
| ~ product(X3,e_1,X0)
| ~ product(X2,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_133,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(e_2,e_1)
| ~ product(X3,e_2,X0)
| ~ product(X3,e_1,X2)
| ~ product(X2,e_1,X1)
| ~ product(X0,e_2,X1) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_134,plain,
( equalish(e_2,e_1)
| ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_133]) ).
tcf(c_207,plain,
! [X0: $i] :
( product(X0,e_2,e_1)
| product(X0,e_1,e_1)
| ~ group_element(e_2)
| ~ group_element(e_1)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_100,c_61]) ).
tcf(c_231,plain,
! [X0: $i] :
( product(X0,e_2,e_1)
| product(X0,e_1,e_1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_207,c_60,c_59]) ).
tcf(c_238,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_231]) ).
tcf(c_245,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_66]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i] :
( equalish(e_2,e_1)
| ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(instantiation,[status(thm)],[c_66]) ).
tcf(c_250,plain,
! [X0: $i] :
( product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_251,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_250]) ).
tcf(c_257,plain,
! [X0: $i] :
( product(e_2,X0,e_2)
| product(e_2,X0,e_1)
| ~ group_element(e_2)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_258,plain,
! [X0: $i] :
( equalish(e_2,e_1)
| ~ product(e_2,X0,e_2)
| ~ product(e_1,X0,e_2) ),
inference(instantiation,[status(thm)],[c_247]) ).
tcf(c_259,plain,
! [X0: $i] :
( equalish(e_1,e_2)
| ~ product(e_2,X0,e_2)
| ~ product(e_1,X0,e_2) ),
inference(instantiation,[status(thm)],[c_245]) ).
tcf(c_260,plain,
( 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_257]) ).
tcf(c_261,plain,
( equalish(e_1,e_2)
| ~ product(e_2,e_1,e_2)
| ~ product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_259]) ).
tcf(c_290,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(e_1,e_2)
| ~ product(e_1,e_2,X2)
| ~ product(X0,e_2,e_1)
| ~ product(e_2,X1,X2)
| ~ product(X0,X1,e_2) ),
inference(instantiation,[status(thm)],[c_120]) ).
tcf(c_295,plain,
( equalish(e_1,e_2)
| ~ product(e_2,e_1,e_1)
| ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_290]) ).
tcf(c_296,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| ~ group_element(e_2) ),
inference(instantiation,[status(thm)],[c_250]) ).
tcf(c_404,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(e_1,e_2)
| ~ product(e_2,e_2,X1)
| ~ product(X2,e_2,e_2)
| ~ product(X2,e_1,X0)
| ~ product(X0,e_1,X1) ),
inference(instantiation,[status(thm)],[c_122]) ).
tcf(c_405,plain,
( equalish(e_1,e_2)
| ~ product(e_2,e_2,e_1)
| ~ product(e_1,e_2,e_2)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_404]) ).
tcf(c_418,plain,
( equalish(e_2,e_1)
| ~ product(e_2,e_2,e_2)
| ~ product(e_1,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_258]) ).
tcf(c_456,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_418,c_405,c_296,c_295,c_261,c_260,c_251,c_238,c_134,c_70,c_61,c_62,c_59,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP131-1.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n018.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 13:49:17 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running EPR theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.68/1.21 % SZS status Started for theBenchmark.p
% 1.68/1.21 % SZS status Unsatisfiable for theBenchmark.p
% 1.68/1.21
% 1.68/1.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.68/1.21
% 1.68/1.21 % ------ iProver source info
% 1.68/1.21
% 1.68/1.21 % git: date: 2026-07-19 20:42:38 +0200
% 1.68/1.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.68/1.21 % git: non_committed_changes: false
% 1.68/1.21
% 1.68/1.21 % ------ Parsing...% successful
% 1.68/1.21
% 1.68/1.21
% 1.68/1.21 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.68/1.21 % ------ Proving...
% 1.68/1.21 % ------ Problem Properties
% 1.68/1.21
% 1.68/1.21 %
% 1.68/1.21 % clauses 10
% 1.68/1.21 % conjectures 2
% 1.68/1.21 % EPR 10
% 1.68/1.21 % Horn 9
% 1.68/1.21 % unary 4
% 1.68/1.21 % binary 0
% 1.68/1.21 % lits 27
% 1.68/1.21 % lits eq 0
% 1.68/1.21 % fd_pure 0
% 1.68/1.21 % fd_pseudo 0
% 1.68/1.21 % fd_cond 0
% 1.68/1.21 % fd_pseudo_cond 0
% 1.68/1.21 % AC symbols 0
% 1.68/1.21
% 1.68/1.21 % ------ Input Options Time Limit: Unbounded
% 1.68/1.21
% 1.68/1.21
% 1.68/1.21 % ------
% 1.68/1.21 % Current options:
% 1.68/1.21 % ------
% 1.68/1.21
% 1.68/1.21
% 1.68/1.21 %
% 1.68/1.21
% 1.68/1.21 % ------ Proving...
% 1.68/1.21 %
% 1.68/1.21
% 1.68/1.21 % SZS status Unsatisfiable for theBenchmark.p
% 1.68/1.21
% 1.68/1.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.68/1.21
% 1.68/1.21
%------------------------------------------------------------------------------