%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP130-1.003 : TPTP v9.3.1. Released v1.2.0.
% 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 01:31:28 PM UTC 2026
% Result : Unsatisfiable 2.17s 1.22s
% Output : CNFRefutation 2.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 107 ( 13 unt; 0 def)
% Number of atoms : 319 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 400 ( 188 ~; 212 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 110 ( 0 sgn 110 !; 0 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).
fof(f2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).
fof(f3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).
fof(f4,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f5,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f7,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
fof(f10,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(f11,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(f12,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(f13,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(f14,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X3,X1,X0)
| ~ product(X0,X2,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).
tcf(c_63,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X3,X1,X0)
| ~ product(X0,X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f13]) ).
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,[],[f12]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_67,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,[],[f10]) ).
tcf(c_70,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[],[f7]) ).
tcf(c_72,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[],[f5]) ).
tcf(c_73,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[],[f4]) ).
tcf(c_74,plain,
group_element(e_1),
inference(cnf_transformation,[],[f1]) ).
tcf(c_75,plain,
group_element(e_3),
inference(cnf_transformation,[],[f3]) ).
tcf(c_76,plain,
group_element(e_2),
inference(cnf_transformation,[],[f2]) ).
tcf(c_78,plain,
( product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_73,c_65]) ).
tcf(c_147,plain,
! [X0: $i,X1: $i] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_73,c_64]) ).
tcf(c_155,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[c_72,c_66]) ).
tcf(c_163,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[c_72,c_65]) ).
tcf(c_164,plain,
( ~ product(e_1,e_3,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_163]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[c_72,c_64]) ).
tcf(c_172,plain,
( ~ product(e_3,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_171]) ).
tcf(c_190,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[c_70,c_65]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i] :
( ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[c_70,c_64]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,X0,e_2)
| ~ product(e_2,X1,X2)
| ~ product(e_2,X0,X1) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_231,plain,
( product(e_1,e_1,e_2)
| ~ product(e_2,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_230]) ).
tcf(c_232,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,e_2,X0)
| ~ product(X0,e_2,X1)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_233,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_2,X1,X0)
| ~ product(X0,X2,e_2)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_234,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,X0,e_3)
| ~ product(e_3,X1,X2)
| ~ product(e_3,X0,X1) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_235,plain,
( product(e_1,e_1,e_3)
| ~ product(e_3,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_234]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,e_3,X0)
| ~ product(X0,e_3,X1)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_237,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_3,X1,X0)
| ~ product(X0,X2,e_3)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_241,plain,
! [X0: $i] :
( product(X0,e_2,e_3)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_243,plain,
( product(e_1,e_2,e_3)
| 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_241]) ).
tcf(c_244,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_67]) ).
tcf(c_245,plain,
! [X0: $i] :
( ~ product(e_2,X0,e_1)
| ~ product(e_1,X0,e_1) ),
inference(instantiation,[status(thm)],[c_147]) ).
tcf(c_246,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_244]) ).
tcf(c_247,plain,
! [X0: $i] :
( product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_250,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_247]) ).
tcf(c_251,plain,
! [X0: $i] :
( product(e_3,X0,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(instantiation,[status(thm)],[c_67]) ).
tcf(c_252,plain,
! [X0: $i] :
( ~ product(e_3,X0,e_1)
| ~ product(e_2,X0,e_1) ),
inference(instantiation,[status(thm)],[c_198]) ).
tcf(c_253,plain,
! [X0: $i] :
( ~ product(e_3,X0,e_1)
| ~ product(e_1,X0,e_1) ),
inference(instantiation,[status(thm)],[c_171]) ).
tcf(c_254,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| ~ group_element(e_3)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_251]) ).
tcf(c_260,plain,
! [X0: $i,X1: $i] :
( product(e_2,X0,e_3)
| ~ product(e_3,X1,e_2)
| ~ product(e_3,X0,X1) ),
inference(instantiation,[status(thm)],[c_234]) ).
tcf(c_265,plain,
! [X0: $i,X1: $i] :
( product(e_3,e_2,X0)
| ~ product(X0,e_2,X1)
| ~ product(X0,X1,e_3) ),
inference(instantiation,[status(thm)],[c_232]) ).
tcf(c_267,plain,
! [X0: $i,X1: $i] :
( product(e_3,e_3,X0)
| ~ product(X0,e_3,X1)
| ~ product(X0,X1,e_3) ),
inference(instantiation,[status(thm)],[c_236]) ).
tcf(c_268,plain,
( product(e_3,e_3,e_1)
| ~ product(e_1,e_3,e_1)
| ~ product(e_1,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_267]) ).
tcf(c_278,plain,
! [X0: $i] :
( ~ product(X0,e_3,e_3)
| ~ product(X0,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_163]) ).
tcf(c_280,plain,
( ~ product(e_1,e_3,e_3)
| ~ product(e_1,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_278]) ).
tcf(c_295,plain,
! [X0: $i] :
( product(e_2,e_3,X0)
| ~ product(X0,e_3,e_2)
| ~ product(X0,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_236]) ).
tcf(c_296,plain,
! [X0: $i] :
( product(e_2,e_2,X0)
| ~ product(X0,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_232]) ).
tcf(c_297,plain,
( product(e_2,e_2,e_1)
| ~ product(e_1,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_296]) ).
tcf(c_298,plain,
( product(e_2,e_3,e_1)
| ~ product(e_1,e_3,e_2)
| ~ product(e_1,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_295]) ).
tcf(c_305,plain,
! [X0: $i] :
( ~ product(X0,e_3,e_2)
| ~ product(X0,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_190]) ).
tcf(c_308,plain,
( ~ product(e_1,e_3,e_2)
| ~ product(e_1,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_305]) ).
tcf(c_354,plain,
( ~ product(e_3,e_3,e_1)
| ~ product(e_1,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_253]) ).
tcf(c_362,plain,
! [X0: $i] :
( product(e_3,X0,e_3)
| ~ product(e_3,e_2,e_3)
| ~ product(e_3,X0,e_2) ),
inference(instantiation,[status(thm)],[c_237]) ).
tcf(c_363,plain,
! [X0: $i] :
( product(e_2,e_3,e_3)
| ~ product(e_3,e_3,X0)
| ~ product(e_3,X0,e_2) ),
inference(instantiation,[status(thm)],[c_236]) ).
tcf(c_366,plain,
( product(e_2,e_3,e_3)
| ~ product(e_3,e_3,e_1)
| ~ product(e_3,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_363]) ).
tcf(c_367,plain,
( product(e_3,e_1,e_3)
| ~ product(e_3,e_2,e_3)
| ~ product(e_3,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_362]) ).
tcf(c_424,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X0,X2,e_2)
| product(X0,X2,e_1)
| product(X1,X2,X0)
| ~ group_element(X2)
| ~ group_element(X0)
| ~ product(X0,e_3,X1) ),
inference(superposition,[status(thm)],[c_67,c_63]) ).
tcf(c_425,plain,
! [X0: $i] :
( product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(X0)
| ~ product(X0,e_1,e_3) ),
inference(superposition,[status(thm)],[c_67,c_139]) ).
tcf(c_438,plain,
! [X0: $i] :
( product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(X0)
| ~ product(X0,e_1,e_3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_425,c_76]) ).
tcf(c_449,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ group_element(e_1)
| ~ product(e_1,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_438]) ).
tcf(c_488,plain,
! [X0: $i] :
( product(e_2,e_3,X0)
| ~ product(X0,e_3,e_1)
| ~ product(X0,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_233]) ).
tcf(c_489,plain,
( product(e_2,e_3,e_1)
| ~ product(e_1,e_3,e_1)
| ~ product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_488]) ).
tcf(c_491,plain,
! [X0: $i] :
( product(e_1,X0,e_3)
| ~ product(e_3,e_3,e_1)
| ~ product(e_3,X0,e_3) ),
inference(instantiation,[status(thm)],[c_234]) ).
tcf(c_493,plain,
( product(e_1,e_1,e_3)
| ~ product(e_3,e_3,e_1)
| ~ product(e_3,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_491]) ).
tcf(c_497,plain,
! [X0: $i] :
( product(e_2,e_2,X0)
| ~ product(X0,e_3,e_2)
| ~ product(X0,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_233]) ).
tcf(c_501,plain,
( product(e_2,e_2,e_1)
| ~ product(e_1,e_3,e_2)
| ~ product(e_1,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_497]) ).
tcf(c_561,plain,
( product(e_2,e_2,e_3)
| ~ product(e_3,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_296]) ).
tcf(c_562,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1)
| ~ group_element(e_3)
| ~ group_element(e_2) ),
inference(instantiation,[status(thm)],[c_251]) ).
tcf(c_624,plain,
! [X0: $i] :
( product(e_2,X0,e_3)
| ~ product(e_3,e_2,e_2)
| ~ product(e_3,X0,e_2) ),
inference(instantiation,[status(thm)],[c_260]) ).
tcf(c_625,plain,
( product(e_2,e_1,e_3)
| ~ product(e_3,e_2,e_2)
| ~ product(e_3,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_624]) ).
tcf(c_643,plain,
( ~ product(e_3,e_3,e_1)
| ~ product(e_2,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_252]) ).
tcf(c_644,plain,
( ~ product(e_2,e_3,e_1)
| ~ product(e_1,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_245]) ).
tcf(c_660,plain,
! [X0: $i] :
( product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(X0)
| ~ product(X0,e_3,e_3) ),
inference(superposition,[status(thm)],[c_67,c_190]) ).
tcf(c_661,plain,
! [X0: $i] :
( product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(X0)
| ~ product(X0,e_3,e_3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_660,c_76]) ).
tcf(c_666,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ group_element(e_1)
| ~ product(e_1,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_661]) ).
tcf(c_683,plain,
( ~ product(e_1,e_3,e_2)
| ~ product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_163]) ).
tcf(c_708,plain,
! [X0: $i] :
( product(e_3,e_2,e_2)
| ~ product(e_2,e_2,X0)
| ~ product(e_2,X0,e_3) ),
inference(instantiation,[status(thm)],[c_265]) ).
tcf(c_709,plain,
( product(e_3,e_2,e_2)
| ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_708]) ).
tcf(c_748,plain,
( ~ product(e_2,e_2,e_3)
| ~ product(e_2,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_155]) ).
tcf(c_751,plain,
! [X0: $i] :
( ~ product(e_3,e_2,X0)
| ~ product(e_2,e_2,X0) ),
inference(instantiation,[status(thm)],[c_198]) ).
tcf(c_754,plain,
( ~ product(e_3,e_2,e_1)
| ~ product(e_2,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_751]) ).
tcf(c_755,plain,
! [X0: $i,X1: $i] :
( product(X1,X0,e_2)
| ~ product(e_2,e_2,X1)
| ~ product(e_2,X0,e_2) ),
inference(instantiation,[status(thm)],[c_230]) ).
tcf(c_756,plain,
( product(e_1,e_1,e_2)
| ~ product(e_2,e_2,e_1)
| ~ product(e_2,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_755]) ).
tcf(c_843,plain,
( product(e_1,e_3,e_1)
| ~ product(e_1,e_3,e_2)
| ~ product(e_1,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_236]) ).
tcf(c_850,plain,
( ~ product(e_3,e_2,e_1)
| ~ product(e_1,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_253]) ).
tcf(c_859,plain,
! [X0: $i] :
( product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| product(X0,e_1,e_2)
| product(X0,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_67,c_438]) ).
tcf(c_860,plain,
! [X0: $i] :
( product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| product(X0,e_1,e_2)
| product(X0,e_1,e_1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_859,c_74]) ).
tcf(c_866,plain,
( product(e_1,e_2,e_2)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_860]) ).
tcf(c_899,plain,
( ~ product(e_2,e_3,e_3)
| ~ product(e_2,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_278]) ).
tcf(c_913,plain,
! [X0: $i,X1: $i] :
( product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| product(e_3,X1,X0)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(e_3)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_67,c_424]) ).
tcf(c_914,plain,
! [X0: $i,X1: $i] :
( product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| product(e_3,X1,X0)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_913,c_75]) ).
tcf(c_1055,plain,
! [X0: $i] :
( product(e_3,e_3,X0)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(equality_factoring,[status(thm)],[c_914]) ).
tcf(c_1057,plain,
! [X0: $i] :
( product(e_3,e_3,X0)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1055,c_75]) ).
tcf(c_1205,plain,
( product(e_3,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| ~ group_element(e_1) ),
inference(instantiation,[status(thm)],[c_1057]) ).
tcf(c_1410,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1205,c_899,c_866,c_850,c_843,c_756,c_754,c_748,c_709,c_683,c_666,c_643,c_644,c_625,c_562,c_561,c_501,c_493,c_489,c_449,c_367,c_366,c_354,c_308,c_298,c_297,c_280,c_268,c_254,c_250,c_246,c_243,c_235,c_231,c_172,c_164,c_78,c_74,c_75,c_76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP130-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n005.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 13:45:32 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running EPR theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 2.17/1.22 % SZS status Started for theBenchmark.p
% 2.17/1.22 % SZS status Unsatisfiable for theBenchmark.p
% 2.17/1.22
% 2.17/1.22 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.17/1.22
% 2.17/1.22 % ------ iProver source info
% 2.17/1.22
% 2.17/1.22 % git: date: 2026-07-19 20:42:38 +0200
% 2.17/1.22 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.17/1.22 % git: non_committed_changes: false
% 2.17/1.22
% 2.17/1.22 % ------ Parsing...% successful
% 2.17/1.22
% 2.17/1.22
% 2.17/1.22 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 2.17/1.22 %
% 2.17/1.22
% 2.17/1.22 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e %
% 2.17/1.22
% 2.17/1.22 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 2.17/1.22 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.17/1.22 % ------ Proving...
% 2.17/1.22 % ------ Problem Properties
% 2.17/1.22
% 2.17/1.22 %
% 2.17/1.22 % clauses 14
% 2.17/1.22 % conjectures 1
% 2.17/1.22 % EPR 14
% 2.17/1.22 % Horn 13
% 2.17/1.22 % unary 3
% 2.17/1.22 % binary 9
% 2.17/1.22 % lits 29
% 2.17/1.22 % lits eq 0
% 2.17/1.22 % fd_pure 0
% 2.17/1.22 % fd_pseudo 0
% 2.17/1.22 % fd_cond 0
% 2.17/1.22 % fd_pseudo_cond 0
% 2.17/1.22 % AC symbols 0
% 2.17/1.22
% 2.17/1.22 % ------ Schedule EPR non Horn non eq is on
% 2.17/1.22
% 2.17/1.22 % ------ no equalities: superposition off
% 2.17/1.22
% 2.17/1.22 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 2.17/1.22
% 2.17/1.22
% 2.17/1.22 % ------
% 2.17/1.22 % Current options:
% 2.17/1.22 % ------
% 2.17/1.22
% 2.17/1.22
% 2.17/1.22 %
% 2.17/1.22
% 2.17/1.22 % ------ Proving...
% 2.17/1.22 %
% 2.17/1.22
% 2.17/1.22 % SZS status Unsatisfiable for theBenchmark.p
% 2.17/1.22
% 2.17/1.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.17/1.22
% 2.17/1.22
%------------------------------------------------------------------------------