%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP129-1.003 : 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 : n003.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 01:31:26 PM UTC 2026
% Result : Unsatisfiable 2.07s 1.20s
% Output : CNFRefutation 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 119 ( 13 unt; 0 def)
% Number of atoms : 389 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 492 ( 222 ~; 270 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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 : 120 ( 0 sgn 120 !; 0 ?; 102 :)
% 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,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
fof(f4,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_2) ).
fof(f5,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_3) ).
fof(f7,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f14,negated_conjecture,
! [X2,X3,X0,X1] :
( product(X2,X0,X3)
| ~ product(X1,X2,X3)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).
tcf(c_63,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( product(X2,X0,X3)
| ~ product(X1,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_131,plain,
! [X0: $i,X1: $i] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[c_73,c_66]) ).
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_140,plain,
( ~ product(e_1,e_2,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_139]) ).
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_148,plain,
( ~ product(e_2,e_1,e_1)
| ~ product(e_1,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_147]) ).
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_231,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,e_2,X2)
| ~ product(e_2,X0,X1)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_235,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X2,X0,e_3)
| ~ product(X1,X2,e_3)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_236,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(X1,e_3,X2)
| ~ product(e_3,X0,X1)
| ~ product(X0,X1,X2) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_238,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_3,X0,X2)
| ~ product(X1,e_3,X2)
| ~ product(X0,X1,e_3) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_243,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_245,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_243]) ).
tcf(c_246,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_248,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_246]) ).
tcf(c_249,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,
! [X0: $i] :
( ~ product(X0,e_3,e_1)
| ~ product(X0,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_190]) ).
tcf(c_251,plain,
! [X0: $i] :
( ~ product(X0,e_3,e_1)
| ~ product(X0,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_163]) ).
tcf(c_252,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_249]) ).
tcf(c_253,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_254,plain,
! [X0: $i] :
( ~ product(e_3,X0,e_1)
| ~ product(e_2,X0,e_1) ),
inference(instantiation,[status(thm)],[c_198]) ).
tcf(c_255,plain,
! [X0: $i] :
( ~ product(e_3,X0,e_1)
| ~ product(e_1,X0,e_1) ),
inference(instantiation,[status(thm)],[c_171]) ).
tcf(c_256,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_253]) ).
tcf(c_257,plain,
! [X0: $i,X1: $i] :
( product(X1,e_3,e_2)
| ~ product(e_3,X0,X1)
| ~ product(X0,X1,e_2) ),
inference(instantiation,[status(thm)],[c_236]) ).
tcf(c_264,plain,
( product(e_1,e_3,e_2)
| ~ product(e_3,e_1,e_1)
| ~ product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_257]) ).
tcf(c_269,plain,
! [X0: $i] :
( ~ product(X0,e_3,e_2)
| ~ product(X0,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_163]) ).
tcf(c_271,plain,
( ~ product(e_1,e_3,e_2)
| ~ product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_269]) ).
tcf(c_272,plain,
! [X0: $i] :
( ~ product(e_3,X0,e_2)
| ~ product(e_1,X0,e_2) ),
inference(instantiation,[status(thm)],[c_171]) ).
tcf(c_274,plain,
( ~ product(e_3,e_1,e_2)
| ~ product(e_1,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_272]) ).
tcf(c_284,plain,
! [X0: $i] :
( ~ product(X0,e_3,e_2)
| ~ product(X0,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_190]) ).
tcf(c_287,plain,
( ~ product(e_1,e_3,e_2)
| ~ product(e_1,e_2,e_2) ),
inference(instantiation,[status(thm)],[c_284]) ).
tcf(c_302,plain,
! [X0: $i] :
( ~ product(e_3,X0,e_2)
| ~ product(e_2,X0,e_2) ),
inference(instantiation,[status(thm)],[c_198]) ).
tcf(c_303,plain,
! [X0: $i] :
( ~ product(e_2,X0,e_2)
| ~ product(e_1,X0,e_2) ),
inference(instantiation,[status(thm)],[c_147]) ).
tcf(c_305,plain,
( ~ product(e_3,e_1,e_2)
| ~ product(e_2,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_302]) ).
tcf(c_307,plain,
! [X0: $i] :
( product(e_3,e_3,e_1)
| ~ product(e_3,X0,e_3)
| ~ product(X0,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_236]) ).
tcf(c_309,plain,
! [X0: $i] :
( product(e_3,e_2,e_1)
| ~ product(e_2,X0,e_3)
| ~ product(X0,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_231]) ).
tcf(c_314,plain,
( product(e_3,e_3,e_1)
| ~ product(e_3,e_1,e_3)
| ~ product(e_1,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_307]) ).
tcf(c_324,plain,
( ~ product(e_3,e_3,e_1)
| ~ product(e_1,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_255]) ).
tcf(c_325,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_2) ),
inference(instantiation,[status(thm)],[c_249]) ).
tcf(c_326,plain,
( ~ product(e_3,e_3,e_1)
| ~ product(e_2,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_254]) ).
tcf(c_335,plain,
! [X0: $i,X1: $i] :
( product(X1,X0,e_1)
| ~ product(e_3,X1,e_1)
| ~ product(X0,e_3,X1) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_336,plain,
( product(e_1,e_1,e_1)
| ~ product(e_3,e_1,e_1)
| ~ product(e_1,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_335]) ).
tcf(c_337,plain,
! [X0: $i] :
( ~ product(e_3,X0,e_2)
| ~ product(e_3,X0,e_1) ),
inference(instantiation,[status(thm)],[c_131]) ).
tcf(c_338,plain,
( ~ product(e_3,e_1,e_2)
| ~ product(e_3,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_348,plain,
( ~ product(e_3,e_3,e_1)
| ~ product(e_3,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_251]) ).
tcf(c_368,plain,
( ~ product(e_3,e_3,e_3)
| ~ product(e_1,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_171]) ).
tcf(c_369,plain,
( product(e_3,e_1,e_1)
| ~ product(e_3,e_3,e_1)
| ~ product(e_1,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_335]) ).
tcf(c_426,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_3,X2,X1)
| product(X2,X0,e_2)
| product(X2,X0,e_1)
| ~ group_element(X2)
| ~ group_element(X0)
| ~ product(X0,e_3,X1) ),
inference(superposition,[status(thm)],[c_67,c_63]) ).
tcf(c_428,plain,
! [X0: $i] :
( product(X0,e_1,e_2)
| product(X0,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X0)
| ~ product(X0,e_3,e_3) ),
inference(superposition,[status(thm)],[c_67,c_163]) ).
tcf(c_435,plain,
! [X0: $i] :
( product(X0,e_1,e_2)
| product(X0,e_1,e_1)
| ~ group_element(X0)
| ~ product(X0,e_3,e_3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_428,c_74]) ).
tcf(c_454,plain,
( product(e_3,e_1,e_1)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1)
| ~ product(e_1,e_3,e_1) ),
inference(instantiation,[status(thm)],[c_426]) ).
tcf(c_465,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_3,X2,X1)
| product(X2,X0,e_2)
| product(X2,X0,e_1)
| ~ group_element(X2)
| ~ group_element(X0)
| ~ product(X0,e_3,X1) ),
inference(superposition,[status(thm)],[c_67,c_63]) ).
tcf(c_495,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1)
| ~ group_element(e_3) ),
inference(instantiation,[status(thm)],[c_253]) ).
tcf(c_526,plain,
! [X0: $i,X1: $i] :
( product(X1,e_3,e_3)
| ~ product(e_3,X0,X1)
| ~ product(X0,X1,e_3) ),
inference(instantiation,[status(thm)],[c_236]) ).
tcf(c_527,plain,
! [X0: $i,X1: $i] :
( product(e_3,X0,e_3)
| ~ product(X1,e_3,e_3)
| ~ product(X0,X1,e_3) ),
inference(instantiation,[status(thm)],[c_235]) ).
tcf(c_528,plain,
! [X0: $i,X1: $i] :
( product(X1,e_2,e_3)
| ~ product(e_2,X0,X1)
| ~ product(X0,X1,e_3) ),
inference(instantiation,[status(thm)],[c_231]) ).
tcf(c_531,plain,
( product(e_1,e_2,e_3)
| ~ product(e_2,e_1,e_1)
| ~ product(e_1,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_528]) ).
tcf(c_547,plain,
! [X0: $i] :
( product(e_1,X0,e_2)
| product(e_1,X0,e_1)
| ~ group_element(e_1)
| ~ group_element(X0)
| ~ product(e_3,X0,e_3) ),
inference(superposition,[status(thm)],[c_67,c_171]) ).
tcf(c_548,plain,
! [X0: $i] :
( product(e_1,X0,e_2)
| product(e_1,X0,e_1)
| ~ group_element(X0)
| ~ product(e_3,X0,e_3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_547,c_74]) ).
tcf(c_553,plain,
( product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1)
| ~ product(e_3,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_548]) ).
tcf(c_636,plain,
! [X0: $i] :
( product(e_3,X0,e_1)
| ~ product(e_2,e_3,e_1)
| ~ product(X0,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_238]) ).
tcf(c_637,plain,
( product(e_3,e_1,e_1)
| ~ product(e_2,e_3,e_1)
| ~ product(e_1,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_636]) ).
tcf(c_693,plain,
( ~ product(e_3,e_1,e_3)
| ~ product(e_3,e_1,e_1) ),
inference(instantiation,[status(thm)],[c_155]) ).
tcf(c_790,plain,
! [X0: $i] :
( ~ product(X0,e_2,e_3)
| ~ product(X0,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_139]) ).
tcf(c_791,plain,
! [X0: $i] :
( ~ product(X0,e_3,e_3)
| ~ product(X0,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_163]) ).
tcf(c_792,plain,
( ~ product(e_1,e_3,e_3)
| ~ product(e_1,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_791]) ).
tcf(c_793,plain,
( ~ product(e_1,e_2,e_3)
| ~ product(e_1,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_790]) ).
tcf(c_848,plain,
( ~ product(e_3,e_3,e_1)
| ~ product(e_3,e_2,e_1) ),
inference(instantiation,[status(thm)],[c_250]) ).
tcf(c_875,plain,
( product(e_3,e_2,e_1)
| ~ product(e_3,e_3,e_1)
| ~ product(e_2,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_309]) ).
tcf(c_888,plain,
! [X0: $i,X1: $i] :
( product(e_3,X1,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(e_3)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_67,c_426]) ).
tcf(c_889,plain,
! [X0: $i,X1: $i] :
( product(e_3,X1,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_888,c_75]) ).
tcf(c_909,plain,
! [X0: $i,X1: $i] :
( product(e_3,X1,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(e_3)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_67,c_465]) ).
tcf(c_910,plain,
! [X0: $i,X1: $i] :
( product(e_3,X1,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_909,c_75]) ).
tcf(c_965,plain,
( ~ product(e_2,e_1,e_3)
| ~ product(e_1,e_1,e_3) ),
inference(instantiation,[status(thm)],[c_147]) ).
tcf(c_988,plain,
! [X0: $i] :
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_889,c_435]) ).
tcf(c_998,plain,
! [X0: $i] :
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,X0,e_3)
| product(X0,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(X0)
| ~ product(X0,e_3,e_2) ),
inference(superposition,[status(thm)],[c_889,c_190]) ).
tcf(c_1001,plain,
! [X0: $i] :
( product(e_3,e_2,e_3)
| product(e_2,X0,e_1)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(e_2)
| ~ group_element(X0)
| ~ product(e_3,X0,e_2) ),
inference(superposition,[status(thm)],[c_889,c_198]) ).
tcf(c_1025,plain,
! [X0: $i] :
( product(e_3,e_2,e_3)
| product(e_2,X0,e_1)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(X0)
| ~ product(e_3,X0,e_2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1001,c_76]) ).
tcf(c_1046,plain,
! [X0: $i] :
( product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_3,X0,e_3)
| product(X0,e_2,e_1)
| ~ group_element(X0)
| ~ product(X0,e_3,e_2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_998,c_76]) ).
tcf(c_1109,plain,
! [X0: $i] :
( product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_988,c_75]) ).
tcf(c_1184,plain,
( product(e_3,e_1,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| product(e_1,e_2,e_1)
| ~ group_element(e_1)
| ~ product(e_1,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_1046]) ).
tcf(c_1186,plain,
( product(e_3,e_2,e_3)
| product(e_2,e_1,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| ~ group_element(e_1)
| ~ product(e_3,e_1,e_2) ),
inference(instantiation,[status(thm)],[c_1025]) ).
tcf(c_1189,plain,
( product(e_3,e_1,e_2)
| product(e_3,e_1,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_1109]) ).
tcf(c_1221,plain,
! [X0: $i,X1: $i,X2: $i] :
( product(e_3,X2,e_2)
| product(e_3,X1,e_3)
| product(X0,e_3,e_1)
| product(X2,X0,e_2)
| product(X2,X0,e_1)
| product(X1,X0,e_2)
| product(X1,X0,e_1)
| ~ group_element(X2)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(superposition,[status(thm)],[c_910,c_465]) ).
tcf(c_1405,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_1,e_3,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_1221]) ).
tcf(c_1431,plain,
( product(e_2,e_3,e_3)
| ~ product(e_3,e_3,e_2)
| ~ product(e_3,e_2,e_3) ),
inference(instantiation,[status(thm)],[c_526]) ).
tcf(c_1433,plain,
( product(e_3,e_3,e_3)
| ~ product(e_3,e_2,e_3)
| ~ product(e_2,e_3,e_3) ),
inference(instantiation,[status(thm)],[c_527]) ).
tcf(c_1498,plain,
( product(e_3,e_3,e_2)
| ~ product(e_3,e_1,e_3)
| ~ product(e_1,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_257]) ).
tcf(c_1505,plain,
( ~ product(e_2,e_3,e_2)
| ~ product(e_1,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_303]) ).
tcf(c_1506,plain,
( ~ product(e_3,e_3,e_2)
| ~ product(e_1,e_3,e_2) ),
inference(instantiation,[status(thm)],[c_272]) ).
tcf(c_1716,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1505,c_1506,c_1498,c_1431,c_1433,c_1405,c_1189,c_1186,c_1184,c_965,c_875,c_848,c_793,c_792,c_693,c_637,c_553,c_531,c_495,c_454,c_369,c_368,c_348,c_338,c_336,c_326,c_325,c_324,c_314,c_305,c_287,c_274,c_271,c_264,c_256,c_252,c_248,c_245,c_172,c_164,c_148,c_140,c_78,c_74,c_75,c_76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP129-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.35 % Computer : n003.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Wed Sep 23 13:46:19 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.39 Running EPR theorem proving
% 0.14/0.39 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
% 0.14/0.40
% 0.14/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.40
% 0.14/0.40 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 2.07/1.20 % SZS status Started for theBenchmark.p
% 2.07/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 2.07/1.20
% 2.07/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.07/1.20
% 2.07/1.20 % ------ iProver source info
% 2.07/1.20
% 2.07/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 2.07/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.07/1.20 % git: non_committed_changes: false
% 2.07/1.20
% 2.07/1.20 % ------ Parsing...% successful
% 2.07/1.20
% 2.07/1.20
% 2.07/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...% ------ preprocesses with Option_epr_non_horn_non_eq
% 2.07/1.20 %
% 2.07/1.20
% 2.07/1.20 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e %
% 2.07/1.20
% 2.07/1.20 % ------ Preprocessing...% ------ preprocesses with Option_epr_non_horn_non_eq
% 2.07/1.20 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.07/1.20 % ------ Proving...
% 2.07/1.20 % ------ Problem Properties
% 2.07/1.20
% 2.07/1.20 %
% 2.07/1.20 % clauses 14
% 2.07/1.20 % conjectures 1
% 2.07/1.20 % EPR 14
% 2.07/1.20 % Horn 13
% 2.07/1.20 % unary 3
% 2.07/1.20 % binary 9
% 2.07/1.20 % lits 29
% 2.07/1.20 % lits eq 0
% 2.07/1.20 % fd_pure 0
% 2.07/1.20 % fd_pseudo 0
% 2.07/1.20 % fd_cond 0
% 2.07/1.20 % fd_pseudo_cond 0
% 2.07/1.20 % AC symbols 0
% 2.07/1.20
% 2.07/1.20 % ------ Schedule EPR non Horn non eq is on
% 2.07/1.20
% 2.07/1.20 % ------ no equalities: superposition off
% 2.07/1.20
% 2.07/1.20 % ------ Input Options "--resolution_flag false" Time Limit: 70.
% 2.07/1.20
% 2.07/1.20
% 2.07/1.20 % ------
% 2.07/1.20 % Current options:
% 2.07/1.20 % ------
% 2.07/1.20
% 2.07/1.20
% 2.07/1.20 %
% 2.07/1.20
% 2.07/1.20 % ------ Proving...
% 2.07/1.20 %
% 2.07/1.20
% 2.07/1.20 % SZS status Unsatisfiable for theBenchmark.p
% 2.07/1.20
% 2.07/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.07/1.20
% 2.07/1.20
%------------------------------------------------------------------------------