%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP131-2.002 : 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 : n007.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 0.66s 6.10s
% Output : CNFRefutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 55 ( 12 unt; 0 def)
% Number of atoms : 176 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 234 ( 113 ~; 121 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 90 ( 0 sgn 90 !; 0 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
next(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_then_e_2) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ greater(X1,X2)
| ~ next(X0,X2)
| ~ product(X0,e_1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_redundancy) ).
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(f7,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
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,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(f13,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_62,plain,
next(e_1,e_2),
inference(cnf_transformation,[],[f1]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ greater(X1,X2)
| ~ next(X0,X2)
| ~ product(X0,e_1,X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_65,plain,
group_element(e_1),
inference(cnf_transformation,[],[f4]) ).
tcf(c_66,plain,
group_element(e_2),
inference(cnf_transformation,[],[f5]) ).
tcf(c_67,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[],[f6]) ).
tcf(c_68,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[],[f7]) ).
tcf(c_69,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_71,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_72,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_73,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,[],[f12]) ).
tcf(c_74,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,[],[f13]) ).
tcf(c_77,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X2,X0)
| product(X2,X1,e_1)
| ~ group_element(X2)
| ~ group_element(X1)
| ~ product(X0,X1,e_2) ),
inference(superposition,[status(thm)],[c_69,c_72]) ).
tcf(c_125,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_74]) ).
tcf(c_126,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_125]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(e_2,e_1)
| ~ product(e_2,X1,X3)
| ~ product(e_1,X2,X3)
| ~ product(X0,X2,e_1)
| ~ product(X0,X1,e_2) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_153,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_74]) ).
tcf(c_221,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_71]) ).
tcf(c_222,plain,
! [X0: $i,X1: $i] :
( equalish(e_2,e_1)
| ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_262,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_72]) ).
tcf(c_263,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_262]) ).
tcf(c_269,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_69]) ).
tcf(c_270,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_269]) ).
tcf(c_278,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_69]) ).
tcf(c_279,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_278]) ).
tcf(c_313,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(e_2,e_1)
| ~ 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_151]) ).
tcf(c_314,plain,
( equalish(e_2,e_1)
| ~ 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_313]) ).
tcf(c_320,plain,
( product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| ~ group_element(e_2) ),
inference(instantiation,[status(thm)],[c_269]) ).
tcf(c_374,plain,
! [X0: $i] :
( equalish(e_2,e_1)
| ~ product(X0,e_2,e_2)
| ~ product(X0,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_222]) ).
tcf(c_375,plain,
! [X0: $i] :
( equalish(e_1,e_2)
| ~ product(X0,e_2,e_2)
| ~ product(X0,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_221]) ).
tcf(c_376,plain,
( equalish(e_1,e_2)
| ~ product(e_1,e_2,e_2)
| ~ product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_375]) ).
tcf(c_399,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X2,X1)
| product(X2,X0,e_1)
| product(X1,X0,e_1)
| ~ group_element(X2)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_69,c_101]) ).
tcf(c_416,plain,
! [X0: $i,X1: $i] :
( product(X0,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X0)
| ~ greater(e_2,X1)
| ~ next(X0,X1) ),
inference(superposition,[status(thm)],[c_69,c_64]) ).
tcf(c_422,plain,
! [X0: $i,X1: $i] :
( product(X0,e_1,e_1)
| ~ group_element(X0)
| ~ greater(e_2,X1)
| ~ next(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_416,c_65]) ).
tcf(c_498,plain,
! [X0: $i] :
( product(e_2,X0,e_1)
| product(e_1,X0,e_1)
| ~ group_element(e_2)
| ~ group_element(e_1)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_399,c_67]) ).
tcf(c_538,plain,
! [X0: $i] :
( product(e_2,X0,e_1)
| product(e_1,X0,e_1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_498,c_66,c_65]) ).
tcf(c_553,plain,
( product(e_2,e_1,e_1)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_538]) ).
tcf(c_606,plain,
( product(e_1,e_1,e_1)
| ~ group_element(e_1)
| ~ greater(e_2,e_2) ),
inference(superposition,[status(thm)],[c_62,c_422]) ).
tcf(c_607,plain,
( product(e_1,e_1,e_1)
| ~ greater(e_2,e_2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_606,c_65]) ).
tcf(c_610,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(e_2,e_1)
| ~ 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_153]) ).
tcf(c_611,plain,
( equalish(e_2,e_1)
| ~ 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_610]) ).
tcf(c_647,plain,
product(e_1,e_1,e_1),
inference(global_subsumption_just,[status(thm)],[c_607,c_66,c_65,c_68,c_67,c_77,c_270,c_314,c_376,c_553]) ).
tcf(c_712,plain,
( equalish(e_2,e_1)
| ~ product(e_2,e_2,e_2)
| ~ product(e_2,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_374]) ).
tcf(c_713,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_712,c_647,c_611,c_320,c_279,c_270,c_263,c_126,c_67,c_68,c_65,c_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP131-2.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.37 % Computer : n007.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 13:45:43 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...
% 0.66/6.10 % SZS status Started for theBenchmark.p
% 0.66/6.10 % SZS status Unsatisfiable for theBenchmark.p
% 0.66/6.10
% 0.66/6.10 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.66/6.10
% 0.66/6.10 % ------ iProver source info
% 0.66/6.10
% 0.66/6.10 % git: date: 2026-07-19 20:42:38 +0200
% 0.66/6.10 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.66/6.10 % git: non_committed_changes: false
% 0.66/6.10
% 0.66/6.10 % ------ Parsing...% successful
% 0.66/6.10
% 0.66/6.10
% 0.66/6.10 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.66/6.10 % ------ Proving...
% 0.66/6.10 % ------ Problem Properties
% 0.66/6.10
% 0.66/6.10 %
% 0.66/6.10 % clauses 13
% 0.66/6.10 % conjectures 2
% 0.66/6.10 % EPR 13
% 0.66/6.10 % Horn 12
% 0.66/6.10 % unary 6
% 0.66/6.10 % binary 0
% 0.66/6.10 % lits 32
% 0.66/6.10 % lits eq 0
% 0.66/6.10 % fd_pure 0
% 0.66/6.10 % fd_pseudo 0
% 0.66/6.10 % fd_cond 0
% 0.66/6.10 % fd_pseudo_cond 0
% 0.66/6.10 % AC symbols 0
% 0.66/6.10
% 0.66/6.10 % ------ Input Options Time Limit: Unbounded
% 0.66/6.10
% 0.66/6.10
% 0.66/6.10 % ------
% 0.66/6.10 % Current options:
% 0.66/6.10 % ------
% 0.66/6.10
% 0.66/6.10
% 0.66/6.10 %
% 0.66/6.10
% 0.66/6.10 % ------ Proving...
% 0.66/6.10 %
% 0.66/6.10
% 0.66/6.10 % SZS status Unsatisfiable for theBenchmark.p
% 0.66/6.10
% 0.66/6.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.66/6.10
% 0.66/6.10
%------------------------------------------------------------------------------