%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP765-1 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:27:14 PM UTC 2026
% Result : Unsatisfiable 85.57s 69.15s
% Output : CNFRefutation 87.16s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_14)
% Comments :
%------------------------------------------------------------------------------
cnf(sos12,axiom,
eta(X1) = product(i(X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).
cnf(sos09,axiom,
i(X1) = difference(X1,one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
cnf(goals,negated_conjecture,
product(i(i(x0)),x1) != product(eta(x0),product(x0,x1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(sos11,axiom,
product(i(X1),X1) = product(X1,j(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).
cnf(sos10,axiom,
j(X1) = quotient(one,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
cnf(sos08,axiom,
difference(product(X1,X2),product(X1,product(X2,X3))) = quotient(quotient(product(X3,product(X1,X2)),X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos08) ).
cnf(sos07,axiom,
difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
cnf(sos05,axiom,
quotient(product(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
cnf(sos06,axiom,
product(quotient(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
cnf(sos04,axiom,
difference(X1,product(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
cnf(sos03,axiom,
product(X1,difference(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
cnf(sos02,axiom,
product(one,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
cnf(sos01,axiom,
product(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
cnf(i_0_13,axiom,
eta(X1) = product(i(X1),X1),
sos12 ).
cnf(i_0_14,axiom,
i(X1) = difference(X1,one),
sos09 ).
cnf(i_0_15,negated_conjecture,
product(i(i(x0)),x1) != product(eta(x0),product(x0,x1)),
goals ).
cnf(i_0_16,plain,
eta(X1) = product(difference(X1,one),X1),
inference(rw,[status(thm)],[i_0_13,c_0_14]) ).
cnf(i_0_17,axiom,
product(i(X1),X1) = product(X1,j(X1)),
sos11 ).
cnf(i_0_18,axiom,
j(X1) = quotient(one,X1),
sos10 ).
cnf(i_0_19,axiom,
difference(product(X1,X2),product(X1,product(X2,X3))) = quotient(quotient(product(X3,product(X1,X2)),X2),X1),
sos08,
[final] ).
cnf(i_0_20,negated_conjecture,
product(difference(difference(x0,one),one),x1) != product(product(difference(x0,one),x0),product(x0,x1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_15,c_0_14]),c_0_14]),c_0_16]),
[final] ).
cnf(i_0_21,axiom,
difference(X1,product(product(X1,X2),X3)) = quotient(product(X2,product(X3,X1)),X1),
sos07,
[final] ).
cnf(i_0_22,plain,
product(difference(X1,one),X1) = product(X1,quotient(one,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_17,c_0_14]),c_0_18]),
[final] ).
cnf(i_0_23,axiom,
quotient(product(X1,X2),X2) = X1,
sos05,
[final] ).
cnf(i_0_24,axiom,
product(quotient(X1,X2),X2) = X1,
sos06,
[final] ).
cnf(i_0_25,axiom,
difference(X1,product(X1,X2)) = X2,
sos04,
[final] ).
cnf(i_0_26,axiom,
product(X1,difference(X1,X2)) = X2,
sos03,
[final] ).
cnf(i_0_27,axiom,
product(one,X1) = X1,
sos02,
[final] ).
cnf(i_0_28,axiom,
product(X1,one) = X1,
sos01,
[final] ).
cnf(i_0_29,axiom,
X1 = X1 ).
cnf(i_0_30,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_31,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_32,axiom,
( X1 != X2
| difference(X1,X3) = difference(X2,X3) ) ).
cnf(i_0_33,axiom,
( X1 != X2
| difference(X3,X1) = difference(X3,X2) ) ).
cnf(i_0_34,axiom,
( X1 != X2
| product(X1,X3) = product(X2,X3) ) ).
cnf(i_0_35,axiom,
( X1 != X2
| product(X3,X1) = product(X3,X2) ) ).
cnf(i_0_36,axiom,
( X1 != X2
| quotient(X1,X3) = quotient(X2,X3) ) ).
cnf(i_0_37,axiom,
( X1 != X2
| quotient(X3,X1) = quotient(X3,X2) ) ).
cnf(i_0_608,plain,
quotient(one,one) = product(one,product(one,difference(one,one))),
inference(scs_inference,[],[i_0_27,i_0_552,i_0_31,i_0_30]) ).
cnf(i_0_618,plain,
product(one,product(one,difference(one,one))) = difference(X1,product(X1,quotient(one,one))),
inference(scs_inference,[],[i_0_27,i_0_468,i_0_31]) ).
cnf(i_0_620,plain,
difference(X1,product(X1,quotient(one,one))) = product(one,product(one,difference(one,one))),
inference(scs_inference,[],[i_0_27,i_0_468,i_0_31,i_0_30]) ).
cnf(i_0_621,plain,
product(one,product(one,difference(one,one))) = product(quotient(quotient(one,one),X1),X1),
inference(scs_inference,[],[i_0_27,i_0_492,i_0_31]) ).
cnf(i_0_623,plain,
product(quotient(quotient(one,one),X1),X1) = product(one,product(one,difference(one,one))),
inference(scs_inference,[],[i_0_27,i_0_492,i_0_31,i_0_30]) ).
cnf(i_0_624,plain,
product(one,product(one,difference(one,one))) = quotient(product(quotient(one,one),X1),X1),
inference(scs_inference,[],[i_0_27,i_0_516,i_0_31]) ).
cnf(i_0_626,plain,
quotient(product(quotient(one,one),X1),X1) = product(one,product(one,difference(one,one))),
inference(scs_inference,[],[i_0_27,i_0_516,i_0_31,i_0_30]) ).
cnf(i_0_639,plain,
product(one,product(quotient(difference(one,one),X1),X1)) = quotient(product(quotient(one,one),X2),X2),
inference(scs_inference,[],[i_0_27,i_0_111,i_0_31]) ).
cnf(i_0_641,plain,
quotient(product(quotient(one,one),X1),X1) = product(one,product(quotient(difference(one,one),X2),X2)),
inference(scs_inference,[],[i_0_27,i_0_111,i_0_31,i_0_30]) ).
cnf(i_0_714,plain,
product(quotient(one,one),one) = product(one,product(one,product(difference(one,one),one))),
inference(scs_inference,[],[i_0_28,i_0_611,i_0_31]) ).
cnf(i_0_716,plain,
product(one,product(one,product(difference(one,one),one))) = product(quotient(one,one),one),
inference(scs_inference,[],[i_0_28,i_0_611,i_0_31,i_0_30]) ).
cnf(i_0_762,plain,
product(product(one,product(difference(one,one),one)),one) = product(one,quotient(one,one)),
inference(scs_inference,[],[i_0_28,i_0_545,i_0_31]) ).
cnf(i_0_764,plain,
product(one,quotient(one,one)) = product(product(one,product(difference(one,one),one)),one),
inference(scs_inference,[],[i_0_28,i_0_545,i_0_31,i_0_30]) ).
cnf(i_0_768,plain,
product(quotient(one,one),one) = product(one,difference(one,one)),
inference(scs_inference,[],[i_0_28,i_0_554,i_0_31]) ).
cnf(i_0_770,plain,
product(one,difference(one,one)) = product(quotient(one,one),one),
inference(scs_inference,[],[i_0_28,i_0_554,i_0_31,i_0_30]) ).
cnf(i_0_801,plain,
product(product(one,product(difference(one,one),one)),one) = product(quotient(one,one),one),
inference(scs_inference,[],[i_0_28,i_0_800,i_0_31]) ).
cnf(i_0_803,plain,
product(quotient(one,one),one) = product(product(one,product(difference(one,one),one)),one),
inference(scs_inference,[],[i_0_28,i_0_800,i_0_31,i_0_30]) ).
cnf(i_0_822,plain,
product(difference(X1,product(X1,quotient(one,one))),one) = product(one,difference(one,one)),
inference(scs_inference,[],[i_0_28,i_0_470,i_0_31]) ).
cnf(i_0_824,plain,
product(one,difference(one,one)) = product(difference(X1,product(X1,quotient(one,one))),one),
inference(scs_inference,[],[i_0_28,i_0_470,i_0_31,i_0_30]) ).
cnf(i_0_828,plain,
product(product(quotient(quotient(one,one),X1),X1),one) = product(one,difference(one,one)),
inference(scs_inference,[],[i_0_28,i_0_494,i_0_31]) ).
cnf(i_0_830,plain,
product(one,difference(one,one)) = product(product(quotient(quotient(one,one),X1),X1),one),
inference(scs_inference,[],[i_0_28,i_0_494,i_0_31,i_0_30]) ).
cnf(i_0_834,plain,
product(quotient(product(quotient(one,one),X1),X1),one) = product(one,difference(one,one)),
inference(scs_inference,[],[i_0_28,i_0_518,i_0_31]) ).
cnf(i_0_836,plain,
product(one,difference(one,one)) = product(quotient(product(quotient(one,one),X1),X1),one),
inference(scs_inference,[],[i_0_28,i_0_518,i_0_31,i_0_30]) ).
cnf(i_0_843,plain,
product(quotient(product(quotient(one,one),X1),X1),one) = product(quotient(difference(one,one),X2),X2),
inference(scs_inference,[],[i_0_28,i_0_113,i_0_31]) ).
cnf(i_0_845,plain,
product(quotient(difference(one,one),X1),X1) = product(quotient(product(quotient(one,one),X2),X2),one),
inference(scs_inference,[],[i_0_28,i_0_113,i_0_31,i_0_30]) ).
cnf(i_0_888,plain,
product(quotient(one,one),one) = product(X1,difference(X1,difference(one,one))),
inference(scs_inference,[],[i_0_28,i_0_314,i_0_31]) ).
cnf(i_0_890,plain,
product(X1,difference(X1,difference(one,one))) = product(quotient(one,one),one),
inference(scs_inference,[],[i_0_28,i_0_314,i_0_31,i_0_30]) ).
cnf(i_0_918,plain,
product(product(X1,difference(X1,quotient(one,one))),one) = product(one,difference(one,one)),
inference(scs_inference,[],[i_0_28,i_0_425,i_0_31]) ).
cnf(i_0_920,plain,
product(one,difference(one,one)) = product(product(X1,difference(X1,quotient(one,one))),one),
inference(scs_inference,[],[i_0_28,i_0_425,i_0_31,i_0_30]) ).
cnf(i_0_1169,plain,
product(quotient(one,one),one) = quotient(product(quotient(one,one),X1),X1),
inference(scs_inference,[],[i_0_573,i_0_798,i_0_528,i_0_1160,i_0_32,i_0_33,i_0_36,i_0_37,i_0_35,i_0_34,i_0_30,i_0_31]) ).
cnf(i_0_1202,plain,
product(X1,product(one,product(one,product(difference(one,one),one)))) = product(X1,quotient(one,one)),
inference(scs_inference,[],[i_0_609,i_0_32,i_0_33,i_0_36,i_0_37,i_0_35]) ).
cnf(i_0_1203,plain,
product(product(one,product(one,product(difference(one,one),one))),X1) = product(quotient(one,one),X1),
inference(scs_inference,[],[i_0_609,i_0_32,i_0_33,i_0_36,i_0_37,i_0_35,i_0_34]) ).
cnf(i_0_1447,plain,
product(X1,product(one,difference(one,one))) = product(X1,product(one,product(one,quotient(one,one)))),
inference(rename_variables,[],[i_0_1166]) ).
cnf(i_0_375,plain,
product(one,quotient(product(difference(one,one),X1),X1)) = quotient(product(quotient(one,one),X2),X2),
inference(scs_inference,[],[i_0_27,i_0_77,i_0_31]) ).
cnf(i_0_377,plain,
quotient(product(quotient(one,one),X1),X1) = product(one,quotient(product(difference(one,one),X2),X2)),
inference(scs_inference,[],[i_0_27,i_0_77,i_0_31,i_0_30]) ).
cnf(i_0_381,plain,
product(one,product(quotient(difference(one,one),X1),X1)) = product(quotient(quotient(one,one),X2),X2),
inference(scs_inference,[],[i_0_27,i_0_125,i_0_31]) ).
cnf(i_0_383,plain,
product(quotient(quotient(one,one),X1),X1) = product(one,product(quotient(difference(one,one),X2),X2)),
inference(scs_inference,[],[i_0_27,i_0_125,i_0_31,i_0_30]) ).
cnf(i_0_384,plain,
product(one,quotient(product(difference(one,one),X1),X1)) = product(quotient(quotient(one,one),X2),X2),
inference(scs_inference,[],[i_0_27,i_0_134,i_0_31]) ).
cnf(i_0_386,plain,
product(quotient(quotient(one,one),X1),X1) = product(one,quotient(product(difference(one,one),X2),X2)),
inference(scs_inference,[],[i_0_27,i_0_134,i_0_31,i_0_30]) ).
cnf(i_0_558,plain,
product(one,product(one,difference(one,one))) = product(one,quotient(one,one)),
inference(scs_inference,[],[i_0_27,i_0_557,i_0_31]) ).
cnf(i_0_560,plain,
product(one,quotient(one,one)) = product(one,product(one,difference(one,one))),
inference(scs_inference,[],[i_0_27,i_0_557,i_0_31,i_0_30]) ).
cnf(i_0_615,plain,
product(one,product(one,product(one,difference(one,one)))) = quotient(one,one),
inference(scs_inference,[],[i_0_27,i_0_606,i_0_31]) ).
cnf(i_0_617,plain,
quotient(one,one) = product(one,product(one,product(one,difference(one,one)))),
inference(scs_inference,[],[i_0_27,i_0_606,i_0_31,i_0_30]) ).
cnf(i_0_636,plain,
product(one,quotient(product(quotient(one,one),X1),X1)) = quotient(product(difference(one,one),X2),X2),
inference(scs_inference,[],[i_0_27,i_0_75,i_0_31]) ).
cnf(i_0_638,plain,
quotient(product(difference(one,one),X1),X1) = product(one,quotient(product(quotient(one,one),X2),X2)),
inference(scs_inference,[],[i_0_27,i_0_75,i_0_31,i_0_30]) ).
cnf(i_0_642,plain,
product(one,product(quotient(quotient(one,one),X1),X1)) = product(quotient(difference(one,one),X2),X2),
inference(scs_inference,[],[i_0_27,i_0_123,i_0_31]) ).
cnf(i_0_644,plain,
product(quotient(difference(one,one),X1),X1) = product(one,product(quotient(quotient(one,one),X2),X2)),
inference(scs_inference,[],[i_0_27,i_0_123,i_0_31,i_0_30]) ).
cnf(i_0_645,plain,
product(one,product(quotient(quotient(one,one),X1),X1)) = quotient(product(difference(one,one),X2),X2),
inference(scs_inference,[],[i_0_27,i_0_132,i_0_31]) ).
cnf(i_0_647,plain,
quotient(product(difference(one,one),X1),X1) = product(one,product(quotient(quotient(one,one),X2),X2)),
inference(scs_inference,[],[i_0_27,i_0_132,i_0_31,i_0_30]) ).
cnf(i_0_711,plain,
product(quotient(one,one),one) = product(one,product(one,difference(one,one))),
inference(scs_inference,[],[i_0_28,i_0_608,i_0_31]) ).
cnf(i_0_713,plain,
product(one,product(one,difference(one,one))) = product(quotient(one,one),one),
inference(scs_inference,[],[i_0_28,i_0_608,i_0_31,i_0_30]) ).
cnf(i_0_771,plain,
product(product(one,difference(one,one)),one) = product(quotient(one,one),one),
inference(scs_inference,[],[i_0_28,i_0_770,i_0_31]) ).
cnf(i_0_773,plain,
product(quotient(one,one),one) = product(product(one,difference(one,one)),one),
inference(scs_inference,[],[i_0_28,i_0_770,i_0_31,i_0_30]) ).
cnf(i_0_780,plain,
product(product(one,difference(one,one)),one) = product(one,quotient(one,one)),
inference(scs_inference,[],[i_0_28,i_0_557,i_0_31]) ).
cnf(i_0_782,plain,
product(one,quotient(one,one)) = product(product(one,difference(one,one)),one),
inference(scs_inference,[],[i_0_28,i_0_557,i_0_31,i_0_30]) ).
cnf(i_0_840,plain,
product(quotient(product(difference(one,one),X1),X1),one) = quotient(product(quotient(one,one),X2),X2),
inference(scs_inference,[],[i_0_28,i_0_77,i_0_31]) ).
cnf(i_0_842,plain,
quotient(product(quotient(one,one),X1),X1) = product(quotient(product(difference(one,one),X2),X2),one),
inference(scs_inference,[],[i_0_28,i_0_77,i_0_31,i_0_30]) ).
cnf(i_0_846,plain,
product(product(quotient(difference(one,one),X1),X1),one) = product(quotient(quotient(one,one),X2),X2),
inference(scs_inference,[],[i_0_28,i_0_125,i_0_31]) ).
cnf(i_0_848,plain,
product(quotient(quotient(one,one),X1),X1) = product(product(quotient(difference(one,one),X2),X2),one),
inference(scs_inference,[],[i_0_28,i_0_125,i_0_31,i_0_30]) ).
cnf(i_0_849,plain,
product(quotient(product(difference(one,one),X1),X1),one) = product(quotient(quotient(one,one),X2),X2),
inference(scs_inference,[],[i_0_28,i_0_134,i_0_31]) ).
cnf(i_0_851,plain,
product(quotient(quotient(one,one),X1),X1) = product(quotient(product(difference(one,one),X2),X2),one),
inference(scs_inference,[],[i_0_28,i_0_134,i_0_31,i_0_30]) ).
cnf(i_0_891,plain,
product(product(X1,difference(X1,difference(one,one))),one) = product(quotient(one,one),one),
inference(scs_inference,[],[i_0_28,i_0_890,i_0_31]) ).
cnf(i_0_893,plain,
product(quotient(one,one),one) = product(product(X1,difference(X1,difference(one,one))),one),
inference(scs_inference,[],[i_0_28,i_0_890,i_0_31,i_0_30]) ).
cnf(i_0_975,plain,
difference(product(one,quotient(one,one)),X1) = difference(product(one,difference(one,one)),X1),
inference(scs_inference,[],[i_0_555,i_0_32]) ).
cnf(i_0_976,plain,
difference(X1,product(one,quotient(one,one))) = difference(X1,product(one,difference(one,one))),
inference(scs_inference,[],[i_0_555,i_0_32,i_0_33]) ).
cnf(i_0_977,plain,
quotient(product(one,quotient(one,one)),X1) = quotient(product(one,difference(one,one)),X1),
inference(scs_inference,[],[i_0_555,i_0_32,i_0_33,i_0_36]) ).
cnf(i_0_978,plain,
quotient(X1,product(one,quotient(one,one))) = quotient(X1,product(one,difference(one,one))),
inference(scs_inference,[],[i_0_555,i_0_32,i_0_33,i_0_36,i_0_37]) ).
cnf(i_0_979,plain,
product(X1,product(one,quotient(one,one))) = product(X1,product(one,difference(one,one))),
inference(scs_inference,[],[i_0_555,i_0_32,i_0_33,i_0_36,i_0_37,i_0_35]) ).
cnf(i_0_980,plain,
product(product(one,quotient(one,one)),X1) = product(product(one,difference(one,one)),X1),
inference(scs_inference,[],[i_0_555,i_0_32,i_0_33,i_0_36,i_0_37,i_0_35,i_0_34]) ).
cnf(i_0_984,plain,
difference(product(quotient(one,one),one),X1) = difference(product(one,difference(one,one)),X1),
inference(scs_inference,[],[i_0_768,i_0_32]) ).
cnf(i_0_985,plain,
difference(X1,product(quotient(one,one),one)) = difference(X1,product(one,difference(one,one))),
inference(scs_inference,[],[i_0_768,i_0_32,i_0_33]) ).
cnf(i_0_986,plain,
quotient(product(quotient(one,one),one),X1) = quotient(product(one,difference(one,one)),X1),
inference(scs_inference,[],[i_0_768,i_0_32,i_0_33,i_0_36]) ).
cnf(i_0_987,plain,
quotient(X1,product(quotient(one,one),one)) = quotient(X1,product(one,difference(one,one))),
inference(scs_inference,[],[i_0_768,i_0_32,i_0_33,i_0_36,i_0_37]) ).
cnf(i_0_988,plain,
product(X1,product(quotient(one,one),one)) = product(X1,product(one,difference(one,one))),
inference(scs_inference,[],[i_0_768,i_0_32,i_0_33,i_0_36,i_0_37,i_0_35]) ).
cnf(i_0_989,plain,
product(product(quotient(one,one),one),X1) = product(product(one,difference(one,one)),X1),
inference(scs_inference,[],[i_0_768,i_0_32,i_0_33,i_0_36,i_0_37,i_0_35,i_0_34]) ).
cnf(i_0_1172,plain,
quotient(product(quotient(one,one),one),X1) = quotient(quotient(product(quotient(one,one),X2),X2),X1),
inference(scs_inference,[],[i_0_1169,i_0_32,i_0_33,i_0_36]) ).
cnf(i_0_1173,plain,
quotient(X1,product(quotient(one,one),one)) = quotient(X1,quotient(product(quotient(one,one),X2),X2)),
inference(scs_inference,[],[i_0_1169,i_0_32,i_0_33,i_0_36,i_0_37]) ).
cnf(i_0_1174,plain,
product(X1,product(quotient(one,one),one)) = product(X1,quotient(product(quotient(one,one),X2),X2)),
inference(scs_inference,[],[i_0_1169,i_0_32,i_0_33,i_0_36,i_0_37,i_0_35]) ).
cnf(i_0_1175,plain,
product(product(quotient(one,one),one),X1) = product(quotient(product(quotient(one,one),X2),X2),X1),
inference(scs_inference,[],[i_0_1169,i_0_32,i_0_33,i_0_36,i_0_37,i_0_35,i_0_34]) ).
cnf(i_0_1187,plain,
product(quotient(one,one),one) = product(X1,difference(X1,difference(one,one))),
inference(rename_variables,[],[i_0_888]) ).
cnf(i_0_561,plain,
product(one,product(one,quotient(one,one))) = product(one,product(one,difference(one,one))),
inference(scs_inference,[],[i_0_27,i_0_560,i_0_31]) ).
cnf(i_0_563,plain,
product(one,product(one,difference(one,one))) = product(one,product(one,quotient(one,one))),
inference(scs_inference,[],[i_0_27,i_0_560,i_0_31,i_0_30]) ).
cnf(i_0_603,plain,
product(one,product(one,product(one,difference(one,one)))) = product(one,quotient(one,one)),
inference(scs_inference,[],[i_0_27,i_0_558,i_0_31]) ).
cnf(i_0_605,plain,
product(one,quotient(one,one)) = product(one,product(one,product(one,difference(one,one)))),
inference(scs_inference,[],[i_0_27,i_0_558,i_0_31,i_0_30]) ).
cnf(i_0_717,plain,
product(quotient(one,one),one) = product(one,product(one,product(one,difference(one,one)))),
inference(scs_inference,[],[i_0_28,i_0_617,i_0_31]) ).
cnf(i_0_719,plain,
product(one,product(one,product(one,difference(one,one)))) = product(quotient(one,one),one),
inference(scs_inference,[],[i_0_28,i_0_617,i_0_31,i_0_30]) ).
cnf(i_0_732,plain,
product(product(one,product(one,difference(one,one))),one) = product(quotient(one,one),one),
inference(scs_inference,[],[i_0_28,i_0_713,i_0_31]) ).
cnf(i_0_734,plain,
product(quotient(one,one),one) = product(product(one,product(one,difference(one,one))),one),
inference(scs_inference,[],[i_0_28,i_0_713,i_0_31,i_0_30]) ).
cnf(i_0_774,plain,
product(product(quotient(one,one),one),one) = product(product(one,difference(one,one)),one),
inference(scs_inference,[],[i_0_28,i_0_773,i_0_31]) ).
cnf(i_0_776,plain,
product(product(one,difference(one,one)),one) = product(product(quotient(one,one),one),one),
inference(scs_inference,[],[i_0_28,i_0_773,i_0_31,i_0_30]) ).
cnf(i_0_783,plain,
product(product(one,quotient(one,one)),one) = product(product(one,difference(one,one)),one),
inference(scs_inference,[],[i_0_28,i_0_782,i_0_31]) ).
cnf(i_0_785,plain,
product(product(one,difference(one,one)),one) = product(product(one,quotient(one,one)),one),
inference(scs_inference,[],[i_0_28,i_0_782,i_0_31,i_0_30]) ).
cnf(i_0_807,plain,
product(product(one,quotient(one,one)),one) = product(one,product(one,difference(one,one))),
inference(scs_inference,[],[i_0_28,i_0_560,i_0_31]) ).
cnf(i_0_809,plain,
product(one,product(one,difference(one,one))) = product(product(one,quotient(one,one)),one),
inference(scs_inference,[],[i_0_28,i_0_560,i_0_31,i_0_30]) ).
cnf(i_0_991,plain,
product(quotient(one,one),one) = product(quotient(product(one,X1),X1),difference(one,one)),
inference(scs_inference,[],[i_0_768,i_0_944,i_0_982,i_0_32,i_0_33,i_0_36,i_0_37,i_0_35,i_0_34,i_0_30,i_0_31]) ).
cnf(i_0_1135,plain,
product(product(one,difference(one,one)),one) = product(one,product(one,difference(one,one))),
inference(scs_inference,[],[i_0_968,i_0_771,i_0_711,i_0_1126,i_0_32,i_0_33,i_0_36,i_0_37,i_0_35,i_0_34,i_0_30,i_0_31]) ).
cnf(i_0_1149,plain,
product(X1,product(product(one,difference(one,one)),one)) = product(X1,product(one,quotient(one,one))),
inference(scs_inference,[],[i_0_780,i_0_32,i_0_33,i_0_36,i_0_37,i_0_35]) ).
cnf(i_0_1150,plain,
product(product(product(one,difference(one,one)),one),X1) = product(product(one,quotient(one,one)),X1),
inference(scs_inference,[],[i_0_780,i_0_32,i_0_33,i_0_36,i_0_37,i_0_35,i_0_34]) ).
cnf(i_0_1188,plain,
product(product(one,quotient(one,one)),X1) = product(product(one,difference(one,one)),X1),
inference(rename_variables,[],[i_0_980]) ).
cnf(i_0_1219,plain,
product(X1,product(one,product(one,product(one,difference(one,one))))) = product(X1,quotient(one,one)),
inference(scs_inference,[],[i_0_615,i_0_32,i_0_33,i_0_36,i_0_37,i_0_35]) ).
cnf(i_0_1220,plain,
product(product(one,product(one,product(one,difference(one,one)))),X1) = product(quotient(one,one),X1),
inference(scs_inference,[],[i_0_615,i_0_32,i_0_33,i_0_36,i_0_37,i_0_35,i_0_34]) ).
cnf(i_0_1257,plain,
quotient(X1,product(one,quotient(one,one))) = quotient(X1,product(one,difference(one,one))),
inference(rename_variables,[],[i_0_978]) ).
cnf(i_0_1275,plain,
quotient(X1,product(quotient(one,one),one)) = quotient(X1,product(one,difference(one,one))),
inference(rename_variables,[],[i_0_987]) ).
cnf(i_0_1726,plain,
product(one,product(one,product(one,difference(one,one)))) = one,
inference(scs_inference,[],[i_0_24,i_0_719,i_0_32,i_0_33,i_0_36,i_0_37,i_0_35,i_0_34,i_0_31]) ).
cnf(i_0_1743,plain,
product(product(one,product(one,difference(one,one))),one) = one,
inference(scs_inference,[],[i_0_24,i_0_722,i_0_732,i_0_32,i_0_33,i_0_36,i_0_37,i_0_35,i_0_34,i_0_31]) ).
cnf(i_0_1728,plain,
difference(product(one,product(one,product(one,difference(one,one)))),X1) = difference(one,X1),
inference(scs_inference,[],[i_0_1726,i_0_32]) ).
cnf(i_0_1729,plain,
difference(X1,product(one,product(one,product(one,difference(one,one))))) = difference(X1,one),
inference(scs_inference,[],[i_0_1726,i_0_32,i_0_33]) ).
cnf(i_0_1730,plain,
quotient(product(one,product(one,product(one,difference(one,one)))),X1) = quotient(one,X1),
inference(scs_inference,[],[i_0_1726,i_0_32,i_0_33,i_0_36]) ).
cnf(i_0_1731,plain,
quotient(X1,product(one,product(one,product(one,difference(one,one))))) = quotient(X1,one),
inference(scs_inference,[],[i_0_1726,i_0_32,i_0_33,i_0_36,i_0_37]) ).
cnf(i_0_1732,plain,
product(X1,product(one,product(one,product(one,difference(one,one))))) = product(X1,one),
inference(scs_inference,[],[i_0_1726,i_0_32,i_0_33,i_0_36,i_0_37,i_0_35]) ).
cnf(i_0_1733,plain,
product(product(one,product(one,product(one,difference(one,one)))),X1) = product(one,X1),
inference(scs_inference,[],[i_0_1726,i_0_32,i_0_33,i_0_36,i_0_37,i_0_35,i_0_34]) ).
cnf(i_0_1785,plain,
difference(quotient(X1,difference(X2,product(X2,X3))),X4) = difference(quotient(X1,X3),X4),
inference(scs_inference,[],[i_0_1748,i_0_1775,i_0_1662,i_0_1690,i_0_1052,i_0_35,i_0_34,i_0_31,i_0_30,i_0_32]) ).
cnf(i_0_1786,plain,
difference(X1,quotient(X2,difference(X3,product(X3,X4)))) = difference(X1,quotient(X2,X4)),
inference(scs_inference,[],[i_0_1748,i_0_1775,i_0_1662,i_0_1690,i_0_1052,i_0_35,i_0_34,i_0_31,i_0_30,i_0_32,i_0_33]) ).
cnf(i_0_1787,plain,
quotient(quotient(X1,difference(X2,product(X2,X3))),X4) = quotient(quotient(X1,X3),X4),
inference(scs_inference,[],[i_0_1748,i_0_1775,i_0_1662,i_0_1690,i_0_1052,i_0_35,i_0_34,i_0_31,i_0_30,i_0_32,i_0_33,i_0_36]) ).
cnf(i_0_1788,plain,
quotient(X1,quotient(X2,difference(X3,product(X3,X4)))) = quotient(X1,quotient(X2,X4)),
inference(scs_inference,[],[i_0_1748,i_0_1775,i_0_1662,i_0_1690,i_0_1052,i_0_35,i_0_34,i_0_31,i_0_30,i_0_32,i_0_33,i_0_36,i_0_37]) ).
cnf(i_0_1792,plain,
product(product(one,product(one,difference(one,one))),one) = product(one,one),
inference(scs_inference,[],[i_0_1750,i_0_1780,i_0_1743,i_0_41,i_0_30,i_0_35,i_0_34,i_0_31]) ).
cnf(i_0_1885,plain,
difference(product(one,X1),X2) = difference(X1,X2),
inference(scs_inference,[],[i_0_27,i_0_1591,i_0_1777,i_0_31,i_0_30,i_0_32]) ).
cnf(i_0_1886,plain,
difference(X1,product(one,X2)) = difference(X1,X2),
inference(scs_inference,[],[i_0_27,i_0_1591,i_0_1777,i_0_31,i_0_30,i_0_32,i_0_33]) ).
cnf(i_0_1887,plain,
quotient(product(one,X1),X2) = quotient(X1,X2),
inference(scs_inference,[],[i_0_27,i_0_1591,i_0_1777,i_0_31,i_0_30,i_0_32,i_0_33,i_0_36]) ).
cnf(i_0_1888,plain,
quotient(X1,product(one,X2)) = quotient(X1,X2),
inference(scs_inference,[],[i_0_27,i_0_1591,i_0_1777,i_0_31,i_0_30,i_0_32,i_0_33,i_0_36,i_0_37]) ).
cnf(i_0_1890,plain,
difference(product(one,X1),X2) = difference(X1,X2),
inference(rename_variables,[],[i_0_1885]) ).
cnf(i_0_1897,plain,
difference(X1,product(one,X2)) = difference(X1,X2),
inference(rename_variables,[],[i_0_1886]) ).
cnf(i_0_1916,plain,
quotient(X1,product(one,X2)) = quotient(X1,X2),
inference(rename_variables,[],[i_0_1888]) ).
cnf(i_0_1802,plain,
product(X1,product(product(one,product(one,difference(one,one))),one)) = product(X1,product(one,one)),
inference(scs_inference,[],[i_0_1797,i_0_1792,i_0_30,i_0_35]) ).
cnf(i_0_1803,plain,
product(product(product(one,product(one,difference(one,one))),one),X1) = product(product(one,one),X1),
inference(scs_inference,[],[i_0_1797,i_0_1792,i_0_30,i_0_35,i_0_34]) ).
cnf(i_0_1804,plain,
product(product(one,product(one,difference(one,one))),one) = product(one,quotient(product(one,X1),X1)),
inference(scs_inference,[],[i_0_1797,i_0_1792,i_0_943,i_0_30,i_0_35,i_0_34,i_0_31]) ).
cnf(i_0_1904,plain,
difference(quotient(product(one,X1),X2),X3) = difference(quotient(X1,X2),X3),
inference(scs_inference,[],[i_0_1887,i_0_1586,i_0_1896,i_0_31,i_0_30,i_0_32]) ).
cnf(i_0_1905,plain,
difference(X1,quotient(product(one,X2),X3)) = difference(X1,quotient(X2,X3)),
inference(scs_inference,[],[i_0_1887,i_0_1586,i_0_1896,i_0_31,i_0_30,i_0_32,i_0_33]) ).
cnf(i_0_1906,plain,
quotient(quotient(product(one,X1),X2),X3) = quotient(quotient(X1,X2),X3),
inference(scs_inference,[],[i_0_1887,i_0_1586,i_0_1896,i_0_31,i_0_30,i_0_32,i_0_33,i_0_36]) ).
cnf(i_0_1907,plain,
quotient(X1,quotient(product(one,X2),X3)) = quotient(X1,quotient(X2,X3)),
inference(scs_inference,[],[i_0_1887,i_0_1586,i_0_1896,i_0_31,i_0_30,i_0_32,i_0_33,i_0_36,i_0_37]) ).
cnf(i_0_1909,plain,
difference(X1,quotient(product(one,X2),X3)) = difference(X1,quotient(X2,X3)),
inference(rename_variables,[],[i_0_1905]) ).
cnf(i_0_1910,plain,
difference(quotient(product(one,X1),X2),X3) = difference(quotient(X1,X2),X3),
inference(rename_variables,[],[i_0_1904]) ).
cnf(i_0_1914,plain,
quotient(quotient(product(one,X1),X2),product(one,X3)) = quotient(quotient(X1,X2),X3),
inference(scs_inference,[],[i_0_1888,i_0_1906,i_0_31]) ).
cnf(i_0_1915,plain,
quotient(quotient(product(one,X1),X2),X3) = quotient(quotient(X1,X2),X3),
inference(rename_variables,[],[i_0_1906]) ).
cnf(i_0_1152,plain,
product(product(one,difference(one,one)),one) = product(one,product(difference(one,one),one)),
inference(scs_inference,[],[i_0_780,i_0_543,i_0_1143,i_0_32,i_0_33,i_0_36,i_0_37,i_0_35,i_0_34,i_0_30,i_0_31]) ).
cnf(i_0_1824,plain,
product(product(X1,difference(X1,X2)),X3) = product(X2,X3),
inference(scs_inference,[],[i_0_26,i_0_1821,i_0_30,i_0_34]) ).
cnf(i_0_1825,plain,
product(product(X1,quotient(one,X1)),product(X1,X2)) != product(difference(difference(X1,one),one),X2),
inference(scs_inference,[],[i_0_26,i_0_1821,i_0_1807,i_0_30,i_0_34,i_0_31]) ).
cnf(i_0_1827,plain,
product(X1,product(X2,difference(X2,X3))) = product(X1,X3),
inference(scs_inference,[],[i_0_26,i_0_1826,i_0_1821,i_0_1807,i_0_30,i_0_34,i_0_31,i_0_35]) ).
cnf(i_0_1828,plain,
product(difference(difference(X1,one),one),X2) != product(product(X1,quotient(one,X1)),product(X1,X2)),
inference(scs_inference,[],[i_0_1825,i_0_30]) ).
cnf(i_0_1831,plain,
difference(product(X1,difference(X1,X2)),X3) = difference(X2,X3),
inference(scs_inference,[],[i_0_26,i_0_1823,i_0_1825,i_0_1011,i_0_30,i_0_31,i_0_32]) ).
cnf(i_0_1832,plain,
difference(X1,product(X2,difference(X2,X3))) = difference(X1,X3),
inference(scs_inference,[],[i_0_26,i_0_1823,i_0_1825,i_0_1011,i_0_30,i_0_31,i_0_32,i_0_33]) ).
cnf(i_0_1833,plain,
quotient(product(X1,difference(X1,X2)),X3) = quotient(X2,X3),
inference(scs_inference,[],[i_0_26,i_0_1823,i_0_1825,i_0_1011,i_0_30,i_0_31,i_0_32,i_0_33,i_0_36]) ).
cnf(i_0_1834,plain,
quotient(X1,product(X2,difference(X2,X3))) = quotient(X1,X3),
inference(scs_inference,[],[i_0_26,i_0_1823,i_0_1825,i_0_1011,i_0_30,i_0_31,i_0_32,i_0_33,i_0_36,i_0_37]) ).
cnf(i_0_1837,plain,
product(X1,product(X2,difference(X2,X3))) = product(X1,X3),
inference(rename_variables,[],[i_0_1827]) ).
cnf(i_0_1843,plain,
difference(product(X1,difference(X1,X2)),product(X3,difference(X3,X4))) = difference(X2,X4),
inference(scs_inference,[],[i_0_1831,i_0_1832,i_0_1799,i_0_30,i_0_31]) ).
cnf(i_0_1844,plain,
difference(X1,product(X2,difference(X2,X3))) = difference(X1,X3),
inference(rename_variables,[],[i_0_1832]) ).
cnf(i_0_1845,plain,
product(X1,difference(product(X2,difference(X2,X3)),X4)) = product(X1,difference(X3,X4)),
inference(scs_inference,[],[i_0_1831,i_0_1832,i_0_1799,i_0_30,i_0_31,i_0_35]) ).
cnf(i_0_1839,plain,
product(product(product(X1,difference(X1,X2)),X3),X4) = product(product(X2,X3),X4),
inference(scs_inference,[],[i_0_1824,i_0_1836,i_0_30,i_0_34]) ).
cnf(i_0_1855,plain,
difference(product(X1,difference(X1,X2)),product(X3,difference(X3,X4))) = difference(X2,X4),
inference(rename_variables,[],[i_0_1843]) ).
cnf(i_0_1859,plain,
product(quotient(X1,product(X2,difference(X2,X3))),X4) = product(quotient(X1,X3),X4),
inference(scs_inference,[],[i_0_1834,i_0_1835,i_0_944,i_0_31,i_0_30,i_0_34]) ).
cnf(i_0_1849,plain,
difference(quotient(product(X1,difference(X1,X2)),X3),X4) = difference(quotient(X2,X3),X4),
inference(scs_inference,[],[i_0_1833,i_0_1806,i_0_1840,i_0_38,i_0_30,i_0_31,i_0_32]) ).
cnf(i_0_1850,plain,
difference(X1,quotient(product(X2,difference(X2,X3)),X4)) = difference(X1,quotient(X3,X4)),
inference(scs_inference,[],[i_0_1833,i_0_1806,i_0_1840,i_0_38,i_0_30,i_0_31,i_0_32,i_0_33]) ).
cnf(i_0_1851,plain,
quotient(quotient(product(X1,difference(X1,X2)),X3),X4) = quotient(quotient(X2,X3),X4),
inference(scs_inference,[],[i_0_1833,i_0_1806,i_0_1840,i_0_38,i_0_30,i_0_31,i_0_32,i_0_33,i_0_36]) ).
cnf(i_0_1852,plain,
quotient(X1,quotient(product(X2,difference(X2,X3)),X4)) = quotient(X1,quotient(X3,X4)),
inference(scs_inference,[],[i_0_1833,i_0_1806,i_0_1840,i_0_38,i_0_30,i_0_31,i_0_32,i_0_33,i_0_36,i_0_37]) ).
cnf(i_0_1894,plain,
product(quotient(X1,product(X2,difference(X2,X3))),X4) = product(quotient(X1,X3),X4),
inference(rename_variables,[],[i_0_1859]) ).
cnf(c_0_1838,plain,
product(product(one,product(one,difference(one,one))),one) = one,
i_0_1743 ).
cnf(c_0_1839,axiom,
product(X1,one) = X1,
i_0_28 ).
cnf(c_0_1840,plain,
product(one,product(one,difference(one,one))) = one,
inference(rw,[status(thm)],[c_0_1838,c_0_1839]) ).
cnf(c_0_1841,axiom,
product(one,X1) = X1,
i_0_27 ).
cnf(c_0_1842,plain,
quotient(one,one) = product(one,product(one,difference(one,one))),
i_0_608 ).
cnf(c_0_1843,plain,
difference(one,one) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1840,c_0_1841]),c_0_1841]) ).
cnf(c_0_1844,plain,
product(quotient(one,one),one) = quotient(product(quotient(one,one),X1),X1),
i_0_1169 ).
cnf(c_0_1845,plain,
quotient(one,one) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1842,c_0_1841]),c_0_1841]),c_0_1843]) ).
cnf(c_0_1846,axiom,
product(quotient(X1,X2),X2) = X1,
i_0_24 ).
cnf(c_0_1847,axiom,
product(X1,difference(X1,X2)) = X2,
i_0_26 ).
cnf(c_0_1848,plain,
difference(X1,product(X1,quotient(one,one))) = product(one,product(one,difference(one,one))),
i_0_620 ).
cnf(c_0_1849,plain,
quotient(X1,X1) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1844,c_0_1845]),c_0_1841]),c_0_1846]) ).
cnf(c_0_1850,plain,
product(difference(difference(X1,one),one),X2) != product(product(X1,quotient(one,X1)),product(X1,X2)),
i_0_1828 ).
cnf(c_0_1851,plain,
difference(one,X1) = X1,
inference(spm,[status(thm)],[c_0_1841,c_0_1847]) ).
cnf(c_0_1852,plain,
difference(X1,X1) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_1848,c_0_1849]),c_0_1839]),c_0_1841]),c_0_1841]),c_0_1843]) ).
cnf(c_0_1853,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_1850,c_0_1851]),c_0_1852]),c_0_1841]),c_0_1849]),c_0_1839]),c_0_1841]),c_0_1841])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP765-1 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33 % Computer : n022.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 19:05:51 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 85.57/69.15 % Version : CSE_E---1.7
% 85.57/69.15 % Problem : theBenchmark.p
% 85.57/69.15 % SZS status Unsatisfiable for theBenchmark.p
% 85.57/69.15 % SZS output start CNFRefutation
% See solution above
% 87.16/70.77 % Total time : 68.802s
%------------------------------------------------------------------------------