%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP780+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n016.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 01:35:24 PM UTC 2026
% Result : Theorem 105.91s 30.43s
% Output : CNFRefutation 105.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 13
% Syntax : Number of formulae : 125 ( 112 unt; 0 def)
% Number of atoms : 148 ( 122 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 60 ( 37 ~; 21 |; 1 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-3 aty)
% Number of variables : 138 ( 0 sgn 138 !; 0 ?; 90 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : difference(X1,product(X1,X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
fof(f2,axiom,
! [X0,X1] : product(X1,difference(X1,X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
fof(f3,axiom,
! [X0,X1] : quotient(product(X1,X0),X0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
fof(f4,axiom,
! [X0,X1] : product(quotient(X1,X0),X0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
fof(f5,axiom,
! [X0,X1,X2,X3] : product(product(X3,X2),product(X1,X0)) = product(product(X3,X1),product(X2,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
fof(f6,axiom,
! [X0] : product(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
fof(f7,axiom,
! [X0,X1] : product(product(product(X1,X0),X0),product(X0,product(X0,X1))) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
fof(f8,axiom,
! [X0,X1,X2] :
( d(X0,X1,X2)
<=> product(X0,X1) = product(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).
fof(f9,axiom,
! [X0,X1,X2] : bigC(X2,X1,X0) = product(product(X2,X1),product(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
fof(f10,axiom,
d(a1,a2,a3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
fof(f11,axiom,
d(b1,b2,b3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).
fof(f12,axiom,
d(c1,c2,c3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).
fof(f13,conjecture,
d(bigC(a1,b3,c2),bigC(a2,b1,c3),bigC(a3,b2,c1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f14,negated_conjecture,
~ d(bigC(a1,b3,c2),bigC(a2,b1,c3),bigC(a3,b2,c1)),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f15,plain,
~ d(bigC(a1,b3,c2),bigC(a2,b1,c3),bigC(a3,b2,c1)),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( ~ d(X0,X1,X2)
| product(X0,X1) = product(X1,X2) )
& ( product(X0,X1) != product(X1,X2)
| d(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f17,plain,
! [X0,X1] : difference(X1,product(X1,X0)) = X0,
inference(cnf_transformation,[],[f1]) ).
fof(f18,plain,
! [X0,X1] : product(X1,difference(X1,X0)) = X0,
inference(cnf_transformation,[],[f2]) ).
fof(f19,plain,
! [X0,X1] : quotient(product(X1,X0),X0) = X1,
inference(cnf_transformation,[],[f3]) ).
fof(f20,plain,
! [X0,X1] : product(quotient(X1,X0),X0) = X1,
inference(cnf_transformation,[],[f4]) ).
fof(f21,plain,
! [X2,X3,X0,X1] : product(product(X3,X2),product(X1,X0)) = product(product(X3,X1),product(X2,X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f22,plain,
! [X0] : product(X0,X0) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f23,plain,
! [X0,X1] : product(product(product(X1,X0),X0),product(X0,product(X0,X1))) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ~ d(X0,X1,X2)
| product(X0,X1) = product(X1,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f25,plain,
! [X2,X0,X1] :
( product(X0,X1) != product(X1,X2)
| d(X0,X1,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f26,plain,
! [X2,X0,X1] : bigC(X2,X1,X0) = product(product(X2,X1),product(X0,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f27,plain,
d(a1,a2,a3),
inference(cnf_transformation,[],[f10]) ).
fof(f28,plain,
d(b1,b2,b3),
inference(cnf_transformation,[],[f11]) ).
fof(f29,plain,
d(c1,c2,c3),
inference(cnf_transformation,[],[f12]) ).
fof(f30,plain,
~ d(bigC(a1,b3,c2),bigC(a2,b1,c3),bigC(a3,b2,c1)),
inference(cnf_transformation,[],[f15]) ).
fof(f31,plain,
~ d(product(product(a1,b3),product(c2,a1)),product(product(a2,b1),product(c3,a2)),product(product(a3,b2),product(c1,a3))),
inference(definition_unfolding,[],[f30,f26,f26,f26]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : difference(X0,product(X0,X1)) = X1,
inference(cnf_transformation,[],[f17]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] : product(X0,difference(X0,X1)) = X1,
inference(cnf_transformation,[],[f18]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : quotient(product(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f19]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : product(quotient(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f20]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : product(product(X0,X1),product(X2,X3)) = product(product(X0,X2),product(X1,X3)),
inference(cnf_transformation,[],[f21]) ).
tcf(c_54,plain,
! [X0: $i] : product(X0,X0) = X0,
inference(cnf_transformation,[],[f22]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : product(product(product(X0,X1),X1),product(X1,product(X1,X0))) = X1,
inference(cnf_transformation,[],[f23]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( d(X0,X1,X2)
| ( product(X0,X1) != product(X1,X2) ) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product(X0,X1) = product(X1,X2) )
| ~ d(X0,X1,X2) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_58,plain,
d(a1,a2,a3),
inference(cnf_transformation,[],[f27]) ).
tcf(c_59,plain,
d(b1,b2,b3),
inference(cnf_transformation,[],[f28]) ).
tcf(c_60,plain,
d(c1,c2,c3),
inference(cnf_transformation,[],[f29]) ).
tcf(c_61,negated_conjecture,
~ d(product(product(a1,b3),product(c2,a1)),product(product(a2,b1),product(c3,a2)),product(product(a3,b2),product(c1,a3))),
inference(cnf_transformation,[],[f31]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product(X0,X1) != product(X1,X2) )
| d(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_56]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( d(X0,X1,X2)
| ( product(X0,X1) != product(X1,X2) ) ),
inference(renaming,[status(thm)],[c_71]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product(X0,X1) = product(X1,X2) )
| ~ d(X0,X1,X2) ),
inference(prop_impl_just,[status(thm)],[c_57]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product(X0,X1) = product(X1,X2) )
| ( X2 != a3 )
| ( X1 != a2 )
| ( X0 != a1 ) ),
inference(resolution_lifted,[status(thm)],[c_73,c_58]) ).
tcf(c_132,plain,
product(a1,a2) = product(a2,a3),
inference(unflattening,[status(thm)],[c_131]) ).
tcf(c_136,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product(X0,X1) = product(X1,X2) )
| ( X2 != b3 )
| ( X1 != b2 )
| ( X0 != b1 ) ),
inference(resolution_lifted,[status(thm)],[c_73,c_59]) ).
tcf(c_137,plain,
product(b1,b2) = product(b2,b3),
inference(unflattening,[status(thm)],[c_136]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product(X0,X1) = product(X1,X2) )
| ( X2 != c3 )
| ( X1 != c2 )
| ( X0 != c1 ) ),
inference(resolution_lifted,[status(thm)],[c_73,c_60]) ).
tcf(c_142,plain,
product(c1,c2) = product(c2,c3),
inference(unflattening,[status(thm)],[c_141]) ).
tcf(c_146,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( product(X0,X1) != product(X1,X2) )
| ( product(product(a3,b2),product(c1,a3)) != X2 )
| ( product(product(a2,b1),product(c3,a2)) != X1 )
| ( product(product(a1,b3),product(c2,a1)) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_72,c_61]) ).
tcf(c_147,plain,
product(product(product(a1,b3),product(c2,a1)),product(product(a2,b1),product(c3,a2))) != product(product(product(a2,b1),product(c3,a2)),product(product(a3,b2),product(c1,a3))),
inference(unflattening,[status(thm)],[c_146]) ).
tcf(c_266,plain,
product(product(product(a1,a2),product(b1,b2)),product(product(c3,a2),product(c1,a3))) != product(product(product(a1,a2),product(b3,b1)),product(product(c2,a1),product(c3,a2))),
inference(demodulation,[status(thm)],[c_147,c_53,c_132]) ).
tcf(c_268,plain,
! [X0: $i] : difference(X0,X0) = X0,
inference(superposition,[status(thm)],[c_54,c_49]) ).
tcf(c_274,plain,
! [X0: $i] : quotient(X0,X0) = X0,
inference(superposition,[status(thm)],[c_54,c_51]) ).
tcf(c_276,plain,
! [X0: $i,X1: $i] : difference(quotient(X0,X1),X0) = X1,
inference(superposition,[status(thm)],[c_52,c_49]) ).
tcf(c_291,plain,
! [X0: $i,X1: $i] : product(product(product(difference(X0,X1),X0),X0),product(X0,X1)) = X0,
inference(superposition,[status(thm)],[c_50,c_55]) ).
tcf(c_361,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : product(product(X0,X1),product(difference(X0,X2),X3)) = product(X2,product(X1,X3)),
inference(superposition,[status(thm)],[c_50,c_53]) ).
tcf(c_365,plain,
! [X0: $i,X1: $i,X2: $i] : product(product(X0,X1),product(X0,X2)) = product(X0,product(X1,X2)),
inference(superposition,[status(thm)],[c_54,c_53]) ).
tcf(c_371,plain,
! [X0: $i,X1: $i,X2: $i] : product(product(X0,X1),product(X2,X1)) = product(product(X0,X2),X1),
inference(superposition,[status(thm)],[c_54,c_53]) ).
tcf(c_389,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] : product(product(X0,product(X1,X2)),product(X3,product(X4,X5))) = product(product(X0,X3),product(product(X1,X4),product(X2,X5))),
inference(superposition,[status(thm)],[c_53,c_53]) ).
tcf(c_410,plain,
! [X0: $i,X1: $i] : product(product(a2,X0),product(a3,X1)) = product(product(a1,a2),product(X0,X1)),
inference(superposition,[status(thm)],[c_132,c_53]) ).
tcf(c_411,plain,
! [X0: $i,X1: $i] : product(product(X0,X1),product(a1,a2)) = product(product(X0,a2),product(X1,a3)),
inference(superposition,[status(thm)],[c_132,c_53]) ).
tcf(c_516,plain,
! [X0: $i,X1: $i] : product(product(c2,X0),product(c3,X1)) = product(product(c1,c2),product(X0,X1)),
inference(superposition,[status(thm)],[c_142,c_53]) ).
tcf(c_519,plain,
product(product(product(a1,a2),product(b1,b2)),product(product(c3,a2),product(c1,a3))) != product(product(product(a1,a2),product(b3,b1)),product(product(c1,c2),product(a1,a2))),
inference(demodulation,[status(thm)],[c_266,c_516]) ).
tcf(c_520,plain,
product(product(product(a1,a2),product(b1,b2)),product(product(c3,a2),product(c1,a3))) != product(product(product(a1,a2),product(b3,b1)),product(product(c1,a2),product(c2,a3))),
inference(demodulation,[status(thm)],[c_519,c_411]) ).
tcf(c_721,plain,
product(product(product(difference(b2,b3),b2),b2),product(b1,b2)) = b2,
inference(superposition,[status(thm)],[c_137,c_291]) ).
tcf(c_722,plain,
product(product(product(difference(c2,c3),c2),c2),product(c1,c2)) = c2,
inference(superposition,[status(thm)],[c_142,c_291]) ).
tcf(c_734,plain,
product(product(product(difference(c2,c3),c2),c1),c2) = c2,
inference(demodulation,[status(thm)],[c_722,c_371]) ).
tcf(c_735,plain,
product(product(product(difference(b2,b3),b2),b1),b2) = b2,
inference(demodulation,[status(thm)],[c_721,c_371]) ).
tcf(c_770,plain,
product(product(difference(c2,c3),c2),c1) = quotient(c2,c2),
inference(superposition,[status(thm)],[c_734,c_51]) ).
tcf(c_776,plain,
product(product(difference(c2,c3),c2),c1) = c2,
inference(demodulation,[status(thm)],[c_770,c_274]) ).
tcf(c_786,plain,
product(difference(c2,c3),c2) = quotient(c2,c1),
inference(superposition,[status(thm)],[c_776,c_51]) ).
tcf(c_1116,plain,
! [X0: $i,X1: $i] : product(product(X0,X1),X0) = product(X0,product(X1,X0)),
inference(superposition,[status(thm)],[c_54,c_365]) ).
tcf(c_1532,plain,
product(product(difference(b2,b3),b2),b1) = quotient(b2,b2),
inference(superposition,[status(thm)],[c_735,c_51]) ).
tcf(c_1539,plain,
product(product(difference(b2,b3),b2),b1) = b2,
inference(demodulation,[status(thm)],[c_1532,c_274]) ).
tcf(c_1628,plain,
product(difference(b2,b3),b2) = quotient(b2,b1),
inference(superposition,[status(thm)],[c_1539,c_51]) ).
tcf(c_1872,plain,
product(product(a1,a2),a2) = product(a2,product(a3,a2)),
inference(superposition,[status(thm)],[c_132,c_1116]) ).
tcf(c_1888,plain,
! [X0: $i,X1: $i] : quotient(product(X0,product(X1,X0)),X0) = product(X0,X1),
inference(superposition,[status(thm)],[c_1116,c_51]) ).
tcf(c_2028,plain,
product(product(a2,product(a3,a2)),product(a2,product(a2,a1))) = a2,
inference(superposition,[status(thm)],[c_1872,c_55]) ).
tcf(c_2030,plain,
product(a2,product(product(a3,a2),product(a2,a1))) = a2,
inference(demodulation,[status(thm)],[c_2028,c_54,c_389]) ).
tcf(c_2284,plain,
! [X0: $i,X1: $i] : product(X0,quotient(X1,X0)) = quotient(product(X0,X1),X0),
inference(superposition,[status(thm)],[c_52,c_1888]) ).
tcf(c_2654,plain,
product(product(a3,a2),product(a2,a1)) = difference(a2,a2),
inference(superposition,[status(thm)],[c_2030,c_49]) ).
tcf(c_2661,plain,
product(product(a3,a2),product(a2,a1)) = a2,
inference(demodulation,[status(thm)],[c_2654,c_268]) ).
tcf(c_2668,plain,
product(product(a3,a2),product(product(a2,a1),product(a3,a2))) = product(a2,product(a3,a2)),
inference(superposition,[status(thm)],[c_2661,c_1116]) ).
tcf(c_2682,plain,
product(product(a3,a1),a2) = product(a2,product(a3,a2)),
inference(demodulation,[status(thm)],[c_2668,c_54,c_365,c_371,c_410]) ).
tcf(c_2930,plain,
product(b2,quotient(b3,b2)) = quotient(product(b1,b2),b2),
inference(superposition,[status(thm)],[c_137,c_2284]) ).
tcf(c_2931,plain,
product(c2,quotient(c3,c2)) = quotient(product(c1,c2),c2),
inference(superposition,[status(thm)],[c_142,c_2284]) ).
tcf(c_2945,plain,
! [X0: $i,X1: $i] : difference(product(X0,quotient(X1,X0)),product(X0,X1)) = X0,
inference(superposition,[status(thm)],[c_2284,c_276]) ).
tcf(c_2948,plain,
product(c2,quotient(c3,c2)) = c1,
inference(demodulation,[status(thm)],[c_2931,c_51]) ).
tcf(c_2949,plain,
product(b2,quotient(b3,b2)) = b1,
inference(demodulation,[status(thm)],[c_2930,c_51]) ).
tcf(c_3032,plain,
difference(c2,c1) = quotient(c3,c2),
inference(superposition,[status(thm)],[c_2948,c_49]) ).
tcf(c_4313,plain,
difference(b2,b1) = quotient(b3,b2),
inference(superposition,[status(thm)],[c_2949,c_49]) ).
tcf(c_4375,plain,
product(difference(c2,c1),c2) = c3,
inference(superposition,[status(thm)],[c_3032,c_52]) ).
tcf(c_4379,plain,
product(difference(b2,b1),b2) = b3,
inference(superposition,[status(thm)],[c_4313,c_52]) ).
tcf(c_4608,plain,
! [X0: $i] : product(product(c2,X0),c3) = product(c1,product(X0,c2)),
inference(superposition,[status(thm)],[c_4375,c_361]) ).
tcf(c_4919,plain,
! [X0: $i] : product(product(b2,X0),b3) = product(b1,product(X0,b2)),
inference(superposition,[status(thm)],[c_4379,c_361]) ).
tcf(c_5743,plain,
quotient(product(a2,product(a3,a2)),a2) = product(a3,a1),
inference(superposition,[status(thm)],[c_2682,c_51]) ).
tcf(c_5751,plain,
product(a1,a2) = product(a3,a1),
inference(demodulation,[status(thm)],[c_5743,c_51,c_132,c_2284]) ).
tcf(c_5831,plain,
quotient(product(a1,a2),a1) = a3,
inference(superposition,[status(thm)],[c_5751,c_51]) ).
tcf(c_5839,plain,
product(a1,quotient(a2,a1)) = a3,
inference(demodulation,[status(thm)],[c_5831,c_2284]) ).
tcf(c_6151,plain,
difference(a1,a3) = quotient(a2,a1),
inference(superposition,[status(thm)],[c_5839,c_49]) ).
tcf(c_6241,plain,
product(difference(a1,a3),a1) = a2,
inference(superposition,[status(thm)],[c_6151,c_52]) ).
tcf(c_6260,plain,
! [X0: $i] : product(product(a1,X0),a2) = product(a3,product(X0,a1)),
inference(superposition,[status(thm)],[c_6241,c_361]) ).
tcf(c_7277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] : product(product(product(X0,X1),X2),product(product(X3,X1),X4)) = product(product(product(X0,X3),X1),product(X2,X4)),
inference(superposition,[status(thm)],[c_371,c_53]) ).
tcf(c_7307,plain,
product(product(product(a1,a2),product(b3,b1)),product(product(c1,a2),product(c2,a3))) != product(product(product(a1,c3),a2),product(product(b1,b2),product(c1,a3))),
inference(demodulation,[status(thm)],[c_520,c_7277]) ).
tcf(c_7308,plain,
product(product(product(a1,a2),product(b3,b1)),product(product(c1,a2),product(c2,a3))) != product(product(a3,product(b1,b2)),product(product(c3,a1),product(c1,a3))),
inference(demodulation,[status(thm)],[c_7307,c_53,c_389,c_6260]) ).
tcf(c_7816,plain,
product(product(a3,product(b1,b2)),product(product(c3,a1),product(c1,a3))) != product(product(a3,product(b3,b1)),product(product(c1,a1),product(c2,a3))),
inference(demodulation,[status(thm)],[c_7308,c_53,c_389,c_7277,c_6260]) ).
tcf(c_8470,plain,
! [X0: $i] : product(c1,product(difference(c2,X0),c2)) = product(X0,c3),
inference(superposition,[status(thm)],[c_50,c_4608]) ).
tcf(c_8698,plain,
! [X0: $i] : product(b1,product(difference(b2,X0),b2)) = product(X0,b3),
inference(superposition,[status(thm)],[c_50,c_4919]) ).
tcf(c_9087,plain,
product(c1,quotient(c2,c1)) = product(c3,c3),
inference(superposition,[status(thm)],[c_786,c_8470]) ).
tcf(c_9113,plain,
product(c1,quotient(c2,c1)) = c3,
inference(demodulation,[status(thm)],[c_9087,c_54]) ).
tcf(c_9220,plain,
difference(c3,product(c1,c2)) = c1,
inference(superposition,[status(thm)],[c_9113,c_2945]) ).
tcf(c_12784,plain,
! [X0: $i,X1: $i] : product(product(c3,X0),product(c1,X1)) = product(product(c1,c2),product(X0,X1)),
inference(superposition,[status(thm)],[c_9220,c_361]) ).
tcf(c_12788,plain,
product(product(a3,product(b1,b2)),product(product(c1,c2),product(a1,a3))) != product(product(a3,product(b3,b1)),product(product(c1,a1),product(c2,a3))),
inference(demodulation,[status(thm)],[c_7816,c_12784]) ).
tcf(c_12789,plain,
product(product(a3,product(b1,b2)),product(product(c1,a1),product(c2,a3))) != product(product(a3,product(b3,b1)),product(product(c1,a1),product(c2,a3))),
inference(demodulation,[status(thm)],[c_12788,c_53]) ).
tcf(c_13371,plain,
product(b1,quotient(b2,b1)) = product(b3,b3),
inference(superposition,[status(thm)],[c_1628,c_8698]) ).
tcf(c_13397,plain,
product(b1,quotient(b2,b1)) = b3,
inference(demodulation,[status(thm)],[c_13371,c_54]) ).
tcf(c_13469,plain,
product(b1,product(quotient(b2,b1),b1)) = product(b3,b1),
inference(superposition,[status(thm)],[c_13397,c_1116]) ).
tcf(c_13489,plain,
product(b1,b2) = product(b3,b1),
inference(demodulation,[status(thm)],[c_13469,c_52]) ).
tcf(c_13505,plain,
product(product(a3,product(b1,b2)),product(product(c1,a1),product(c2,a3))) != product(product(a3,product(b1,b2)),product(product(c1,a1),product(c2,a3))),
inference(demodulation,[status(thm)],[c_12789,c_13489]) ).
tcf(c_13506,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_13505]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP780+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 16:06:26 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 105.91/30.43 % SZS status Started for theBenchmark.p
% 105.91/30.43 % SZS status Theorem for theBenchmark.p
% 105.91/30.43
% 105.91/30.43 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 105.91/30.43
% 105.91/30.43 % ------ iProver source info
% 105.91/30.43
% 105.91/30.43 % git: date: 2026-07-19 20:42:38 +0200
% 105.91/30.43 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 105.91/30.43 % git: non_committed_changes: false
% 105.91/30.43
% 105.91/30.43 % ------ Parsing...
% 105.91/30.43 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 105.91/30.43
% 105.91/30.43 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e %
% 105.91/30.43
% 105.91/30.43 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 105.91/30.43
% 105.91/30.43 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 105.91/30.43 % ------ Proving...
% 105.91/30.43 % ------ Problem Properties
% 105.91/30.43
% 105.91/30.43 %
% 105.91/30.43 % clauses 14
% 105.91/30.43 % conjectures 0
% 105.91/30.43 % EPR 0
% 105.91/30.43 % Horn 14
% 105.91/30.43 % unary 11
% 105.91/30.43 % binary 0
% 105.91/30.43 % lits 20
% 105.91/30.43 % lits eq 20
% 105.91/30.43 % fd_pure 0
% 105.91/30.43 % fd_pseudo 0
% 105.91/30.43 % fd_cond 0
% 105.91/30.43 % fd_pseudo_cond 0
% 105.91/30.43 % AC symbols 0
% 105.91/30.43
% 105.91/30.43 % ------ Input Options Time Limit: Unbounded
% 105.91/30.43
% 105.91/30.43
% 105.91/30.43 % ------
% 105.91/30.43 % Current options:
% 105.91/30.43 % ------
% 105.91/30.43
% 105.91/30.43
% 105.91/30.43 %
% 105.91/30.43
% 105.91/30.43 % ------ Proving...
% 105.91/30.43 %
% 105.91/30.43
% 105.91/30.43 % SZS status Theorem for theBenchmark.p
% 105.91/30.43
% 105.91/30.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 105.91/30.43
% 105.91/30.43
%------------------------------------------------------------------------------