%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP135-2.002 : 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 : n014.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 01:31:32 PM UTC 2026
% Result : Unsatisfiable 1.81s 1.20s
% Output : CNFRefutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 29 ( 7 unt; 0 def)
% Number of atoms : 107 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 131 ( 53 ~; 78 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 55 ( 0 sgn 55 !; 0 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f5,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f6,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f8,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(f10,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(f11,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(f12,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X3,X0,X1)
| ~ product(X2,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,[],[f4]) ).
tcf(c_65,plain,
group_element(e_2),
inference(cnf_transformation,[],[f5]) ).
tcf(c_66,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[],[f6]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_72,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X3,X0,X1)
| ~ product(X2,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X0,X2,e_1)
| product(X1,X0,X2)
| ~ group_element(X2)
| ~ group_element(X0)
| ~ product(e_2,X0,X1) ),
inference(superposition,[status(thm)],[c_68,c_72]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i] :
( product(e_2,X0,e_1)
| product(e_2,X0,X1)
| product(X0,X1,e_1)
| ~ group_element(e_2)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_68,c_84]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( product(e_2,X0,e_1)
| product(e_2,X0,X1)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_139,c_65]) ).
tcf(c_144,plain,
! [X0: $i,X1: $i] :
( equalish(e_1,e_2)
| ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(instantiation,[status(thm)],[c_70]) ).
tcf(c_145,plain,
( equalish(e_1,e_2)
| ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_144]) ).
tcf(c_146,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_71]) ).
tcf(c_147,plain,
( equalish(e_1,e_2)
| ~ product(e_2,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_146]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_2,X0,X1)
| product(e_1,X0,X2)
| product(X0,X2,e_1)
| product(X0,X1,e_1)
| ~ group_element(X2)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_140,c_84]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_2,X2,e_1)
| product(X2,X0,e_1)
| product(X1,e_2,X2)
| ~ group_element(X2)
| ~ group_element(X0)
| ~ product(X0,e_2,X1) ),
inference(superposition,[status(thm)],[c_140,c_72]) ).
tcf(c_286,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(e_1,X0,X2)
| product(X0,X3,e_1)
| product(X0,X2,e_1)
| product(X0,X1,e_1)
| product(X1,X0,X3)
| ~ group_element(X3)
| ~ group_element(X2)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_158,c_84]) ).
tcf(c_287,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_2,X2,e_1)
| product(e_2,X1,e_1)
| product(e_2,X0,e_1)
| product(e_1,e_2,X1)
| product(X2,e_2,e_1)
| product(X0,e_2,X2)
| ~ group_element(e_2)
| ~ group_element(X2)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_158,c_163]) ).
tcf(c_344,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_2,X2,e_1)
| product(e_2,X1,e_1)
| product(e_2,X0,e_1)
| product(e_1,e_2,X1)
| product(X2,e_2,e_1)
| product(X0,e_2,X2)
| ~ group_element(X2)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_287,c_65]) ).
tcf(c_351,plain,
( product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_286]) ).
tcf(c_352,plain,
( product(e_2,e_1,e_1)
| product(e_1,e_2,e_1)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_344]) ).
tcf(c_353,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_352,c_351,c_147,c_145,c_66,c_64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP135-2.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 13:49:48 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running EPR theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 1.81/1.20 % SZS status Started for theBenchmark.p
% 1.81/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 1.81/1.20
% 1.81/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.81/1.20
% 1.81/1.20 % ------ iProver source info
% 1.81/1.20
% 1.81/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 1.81/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.81/1.20 % git: non_committed_changes: false
% 1.81/1.20
% 1.81/1.20 % ------ Parsing...% successful
% 1.81/1.20
% 1.81/1.20
% 1.81/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.81/1.20 % ------ Proving...
% 1.81/1.20 % ------ Problem Properties
% 1.81/1.20
% 1.81/1.20 %
% 1.81/1.20 % clauses 12
% 1.81/1.20 % conjectures 1
% 1.81/1.20 % EPR 12
% 1.81/1.20 % Horn 11
% 1.81/1.20 % unary 6
% 1.81/1.20 % binary 0
% 1.81/1.20 % lits 25
% 1.81/1.20 % lits eq 0
% 1.81/1.20 % fd_pure 0
% 1.81/1.20 % fd_pseudo 0
% 1.81/1.20 % fd_cond 0
% 1.81/1.20 % fd_pseudo_cond 0
% 1.81/1.20 % AC symbols 0
% 1.81/1.20
% 1.81/1.20 % ------ Input Options Time Limit: Unbounded
% 1.81/1.20
% 1.81/1.20
% 1.81/1.20 % ------
% 1.81/1.20 % Current options:
% 1.81/1.20 % ------
% 1.81/1.20
% 1.81/1.20
% 1.81/1.20 %
% 1.81/1.20
% 1.81/1.20 % ------ Proving...
% 1.81/1.20 %
% 1.81/1.20
% 1.81/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 1.81/1.20
% 1.81/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.81/1.20
% 1.81/1.20
%------------------------------------------------------------------------------