%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP123-8.003 : 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 : 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 01:31:08 PM UTC 2026
% Result : Unsatisfiable 1.99s 6.24s
% Output : CNFRefutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 47 ( 19 unt; 0 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 118 ( 60 ~; 58 |; 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 : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 58 ( 0 sgn 58 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
fof(f18,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
fof(f19,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f20,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f21,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f26,axiom,
! [X0,X1] :
( product1(X0,X1,e_3)
| product1(X0,X1,e_2)
| product1(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_total_function1) ).
fof(f28,axiom,
! [X2,X3,X0,X1] :
( equalish(X1,X3)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_right_cancellation) ).
fof(f29,axiom,
! [X2,X3,X0,X1] :
( equalish(X0,X3)
| ~ product1(X3,X1,X2)
| ~ product1(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_left_cancellation) ).
fof(f30,axiom,
! [X0] : product1(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product1_idempotence) ).
fof(f32,axiom,
! [X2,X3,X0,X1] :
( equalish(X2,X3)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_total_function2) ).
fof(f35,axiom,
! [X0] : product2(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product2_idempotence) ).
fof(f36,negated_conjecture,
! [X2,X3,X0,X1] :
( product2(X3,X0,X1)
| ~ product1(X2,X1,X3)
| ~ product1(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg1a) ).
tcf(c_85,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product2(X3,X0,X1)
| ~ product1(X2,X1,X3)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_86,plain,
! [X0: $i] : product1(X0,X0,X0),
inference(cnf_transformation,[],[f30]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X0,X3)
| ~ product1(X3,X1,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X1,X3)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i] :
( product1(X1,X0,e_3)
| product1(X1,X0,e_2)
| product1(X1,X0,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_91,plain,
! [X0: $i] : product2(X0,X0,X0),
inference(cnf_transformation,[],[f35]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X2,X3)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_100,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[],[f21]) ).
tcf(c_101,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[],[f20]) ).
tcf(c_108,plain,
group_element(e_3),
inference(cnf_transformation,[],[f19]) ).
tcf(c_109,plain,
group_element(e_2),
inference(cnf_transformation,[],[f18]) ).
tcf(c_110,plain,
group_element(e_1),
inference(cnf_transformation,[],[f17]) ).
tcf(c_120,plain,
product1(e_1,e_1,e_1),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_399,plain,
! [X0: $i,X1: $i] :
( ~ product1(e_2,X0,X1)
| ~ product1(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_101,c_87]) ).
tcf(c_400,plain,
( ~ product1(e_2,e_1,e_1)
| ~ product1(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_399]) ).
tcf(c_415,plain,
! [X0: $i,X1: $i] :
( ~ product1(X0,e_2,X1)
| ~ product1(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_101,c_88]) ).
tcf(c_423,plain,
! [X0: $i,X1: $i] :
( ~ product2(X0,X1,e_2)
| ~ product2(X0,X1,e_1) ),
inference(resolution,[status(thm)],[c_101,c_94]) ).
tcf(c_447,plain,
! [X0: $i,X1: $i] :
( ~ product1(e_3,X0,X1)
| ~ product1(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_100,c_87]) ).
tcf(c_448,plain,
( ~ product1(e_3,e_1,e_1)
| ~ product1(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_447]) ).
tcf(c_463,plain,
! [X0: $i,X1: $i] :
( ~ product1(X0,e_3,X1)
| ~ product1(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_100,c_88]) ).
tcf(c_620,plain,
product2(e_2,e_2,e_2),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_623,plain,
product1(e_2,e_2,e_2),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_626,plain,
! [X0: $i,X1: $i,X2: $i] :
( product2(X2,e_2,X1)
| ~ product1(e_2,X1,X0)
| ~ product1(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_85]) ).
tcf(c_633,plain,
product1(e_3,e_3,e_3),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_649,plain,
! [X0: $i] :
( product1(e_2,X0,e_3)
| product1(e_2,X0,e_2)
| product1(e_2,X0,e_1)
| ~ group_element(e_2)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_651,plain,
( product1(e_2,e_1,e_3)
| product1(e_2,e_1,e_2)
| product1(e_2,e_1,e_1)
| ~ group_element(e_2)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_649]) ).
tcf(c_655,plain,
! [X0: $i] :
( product1(e_3,X0,e_3)
| product1(e_3,X0,e_2)
| product1(e_3,X0,e_1)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_90]) ).
tcf(c_658,plain,
( product1(e_3,e_1,e_3)
| product1(e_3,e_1,e_2)
| product1(e_3,e_1,e_1)
| ~ group_element(e_3)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_655]) ).
tcf(c_730,plain,
( ~ product2(e_2,e_2,e_2)
| ~ product2(e_2,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_423]) ).
tcf(c_737,plain,
( ~ product1(e_2,e_2,e_2)
| ~ product1(e_2,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_415]) ).
tcf(c_752,plain,
( ~ product1(e_3,e_3,e_3)
| ~ product1(e_3,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_463]) ).
tcf(c_786,plain,
! [X0: $i,X1: $i] :
( product2(X1,e_2,X0)
| ~ product1(e_2,X0,e_3)
| ~ product1(e_3,X0,X1) ),
inference(instantiation,[status(thm)],[c_626]) ).
tcf(c_913,plain,
! [X0: $i] :
( product2(e_2,e_2,X0)
| ~ product1(e_3,X0,e_2)
| ~ product1(e_2,X0,e_3) ),
inference(instantiation,[status(thm)],[c_786]) ).
tcf(c_914,plain,
( product2(e_2,e_2,e_1)
| ~ product1(e_3,e_1,e_2)
| ~ product1(e_2,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_913]) ).
tcf(c_915,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_914,c_752,c_737,c_730,c_658,c_651,c_633,c_623,c_620,c_448,c_400,c_120,c_108,c_109,c_110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-8.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.37 % Computer : n011.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Wed Sep 23 13:36:47 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.41 Running EPR theorem proving
% 0.13/5.41 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
% 0.13/5.42
% 0.13/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.42
% 0.13/5.42 % Detected problem language: tptp
% 0.13/5.43 % Proving...
% 1.99/6.24 % SZS status Started for theBenchmark.p
% 1.99/6.24 % SZS status Unsatisfiable for theBenchmark.p
% 1.99/6.24
% 1.99/6.24 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.99/6.24
% 1.99/6.24 % ------ iProver source info
% 1.99/6.24
% 1.99/6.24 % git: date: 2026-07-19 20:42:38 +0200
% 1.99/6.24 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.99/6.24 % git: non_committed_changes: false
% 1.99/6.24
% 1.99/6.24 % ------ Parsing...% successful
% 1.99/6.24
% 1.99/6.24
% 1.99/6.24 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 1.99/6.24 %
% 1.99/6.24
% 1.99/6.24 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e %
% 1.99/6.24
% 1.99/6.24 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 1.99/6.24 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.99/6.24 % ------ Proving...
% 1.99/6.24 % ------ Problem Properties
% 1.99/6.24
% 1.99/6.24 %
% 1.99/6.24 % clauses 47
% 1.99/6.24 % conjectures 1
% 1.99/6.24 % EPR 47
% 1.99/6.24 % Horn 44
% 1.99/6.24 % unary 15
% 1.99/6.24 % binary 21
% 1.99/6.24 % lits 104
% 1.99/6.24 % lits eq 0
% 1.99/6.24 % fd_pure 0
% 1.99/6.24 % fd_pseudo 0
% 1.99/6.24 % fd_cond 0
% 1.99/6.24 % fd_pseudo_cond 0
% 1.99/6.24 % AC symbols 0
% 1.99/6.24
% 1.99/6.24 % ------ Schedule EPR non Horn non eq is on
% 1.99/6.24
% 1.99/6.24 % ------ no equalities: superposition off
% 1.99/6.24
% 1.99/6.24 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 1.99/6.24
% 1.99/6.24
% 1.99/6.24 % ------
% 1.99/6.24 % Current options:
% 1.99/6.24 % ------
% 1.99/6.24
% 1.99/6.24
% 1.99/6.24 %
% 1.99/6.24
% 1.99/6.24 % ------ Proving...
% 1.99/6.24 %
% 1.99/6.24
% 1.99/6.24 % SZS status Unsatisfiable for theBenchmark.p
% 1.99/6.24
% 1.99/6.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.99/6.24
% 1.99/6.24
%------------------------------------------------------------------------------