%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT390-1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n015.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 04:38:27 PM UTC 2026
% Result : Unsatisfiable 119.38s 75.40s
% Output : CNFRefutation 119.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 2
% Syntax : Number of clauses : 61 ( 61 unt; 0 nHn; 3 RR)
% Number of literals : 61 ( 60 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 168 ( 53 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sos,axiom,
mult(plus(mult(plus(X1,X2),plus(X2,mult(X1,X2))),X3),plus(mult(plus(X1,mult(mult(plus(X4,X2),plus(X2,X5)),X2)),plus(mult(plus(X2,plus(plus(mult(X4,mult(X2,X5)),mult(X6,X2)),X2)),plus(X7,mult(X2,plus(plus(mult(X2,X8),mult(X6,X2)),X2)))),mult(X1,mult(mult(plus(X4,X2),plus(X2,X5)),X2)))),mult(mult(plus(X1,X2),plus(X2,mult(X1,X2))),X3))) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos) ).
cnf(goals,negated_conjecture,
plus(a,mult(b,mult(a,c))) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c_0_2,axiom,
mult(plus(mult(plus(X1,X2),plus(X2,mult(X1,X2))),X3),plus(mult(plus(X1,mult(mult(plus(X4,X2),plus(X2,X5)),X2)),plus(mult(plus(X2,plus(plus(mult(X4,mult(X2,X5)),mult(X6,X2)),X2)),plus(X7,mult(X2,plus(plus(mult(X2,X8),mult(X6,X2)),X2)))),mult(X1,mult(mult(plus(X4,X2),plus(X2,X5)),X2)))),mult(mult(plus(X1,X2),plus(X2,mult(X1,X2))),X3))) = X2,
sos ).
cnf(c_0_3,plain,
mult(plus(mult(plus(X1,mult(plus(X2,X3),plus(X3,mult(X2,X3)))),plus(mult(plus(X2,X3),plus(X3,mult(X2,X3))),mult(X1,mult(plus(X2,X3),plus(X3,mult(X2,X3)))))),X4),plus(mult(plus(X1,mult(mult(plus(mult(plus(X2,X3),plus(X3,mult(X2,X3))),mult(plus(X2,X3),plus(X3,mult(X2,X3)))),plus(mult(plus(X2,X3),plus(X3,mult(X2,X3))),X5)),mult(plus(X2,X3),plus(X3,mult(X2,X3))))),plus(X3,mult(X1,mult(mult(plus(mult(plus(X2,X3),plus(X3,mult(X2,X3))),mult(plus(X2,X3),plus(X3,mult(X2,X3)))),plus(mult(plus(X2,X3),plus(X3,mult(X2,X3))),X5)),mult(plus(X2,X3),plus(X3,mult(X2,X3))))))),mult(mult(plus(X1,mult(plus(X2,X3),plus(X3,mult(X2,X3)))),plus(mult(plus(X2,X3),plus(X3,mult(X2,X3))),mult(X1,mult(plus(X2,X3),plus(X3,mult(X2,X3)))))),X4))) = mult(plus(X2,X3),plus(X3,mult(X2,X3))),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
mult(plus(mult(plus(X1,X2),plus(X2,mult(X1,X2))),X3),plus(mult(plus(X1,mult(mult(plus(X2,X2),plus(X2,X4)),X2)),plus(mult(plus(X5,mult(mult(plus(X6,X2),plus(X2,X7)),X2)),plus(mult(plus(X2,plus(plus(mult(X6,mult(X2,X7)),mult(X8,X2)),X2)),plus(X9,mult(X2,plus(plus(mult(X2,X10),mult(X8,X2)),X2)))),mult(X5,mult(mult(plus(X6,X2),plus(X2,X7)),X2)))),mult(X1,mult(mult(plus(X2,X2),plus(X2,X4)),X2)))),mult(mult(plus(X1,X2),plus(X2,mult(X1,X2))),X3))) = X2,
inference(spm,[status(thm)],[c_0_3,c_0_2]) ).
cnf(c_0_5,plain,
mult(plus(mult(plus(mult(plus(X1,X2),plus(X2,mult(X1,X2))),X2),plus(X2,mult(mult(plus(X1,X2),plus(X2,mult(X1,X2))),X2))),X3),plus(X2,mult(mult(plus(mult(plus(X1,X2),plus(X2,mult(X1,X2))),X2),plus(X2,mult(mult(plus(X1,X2),plus(X2,mult(X1,X2))),X2))),X3))) = X2,
inference(spm,[status(thm)],[c_0_4,c_0_2]) ).
cnf(c_0_6,plain,
mult(plus(mult(plus(X1,X2),plus(X2,mult(X1,X2))),X3),plus(mult(plus(X1,mult(mult(plus(X2,X2),plus(X2,X4)),X2)),plus(X2,mult(X1,mult(mult(plus(X2,X2),plus(X2,X4)),X2)))),mult(mult(plus(X1,X2),plus(X2,mult(X1,X2))),X3))) = X2,
inference(spm,[status(thm)],[c_0_3,c_0_5]) ).
cnf(c_0_7,plain,
mult(plus(X1,X2),plus(X1,mult(X1,X2))) = X1,
inference(spm,[status(thm)],[c_0_5,c_0_5]) ).
cnf(c_0_8,plain,
mult(plus(X1,mult(mult(plus(X2,X2),plus(X2,X3)),X2)),plus(X2,mult(X1,mult(mult(plus(X2,X2),plus(X2,X3)),X2)))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_6]),c_0_6]),c_0_6]),c_0_7]) ).
cnf(c_0_9,plain,
mult(plus(mult(plus(X1,X2),plus(X2,mult(X1,X2))),X3),plus(X2,mult(mult(plus(X1,X2),plus(X2,mult(X1,X2))),X3))) = X2,
inference(rw,[status(thm)],[c_0_6,c_0_8]) ).
cnf(c_0_10,plain,
mult(plus(X1,mult(mult(plus(X2,X3),plus(X3,X4)),X3)),plus(mult(plus(X3,plus(plus(mult(X2,mult(X3,X4)),mult(X5,X3)),X3)),plus(X6,mult(X3,plus(plus(mult(X3,X7),mult(X5,X3)),X3)))),mult(X1,mult(mult(plus(X2,X3),plus(X3,X4)),X3)))) = X3,
inference(spm,[status(thm)],[c_0_2,c_0_8]) ).
cnf(c_0_11,plain,
mult(plus(X1,plus(plus(mult(X2,mult(X1,X3)),mult(X4,X1)),X1)),plus(X5,mult(X1,plus(plus(mult(X1,X6),mult(X4,X1)),X1)))) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,plain,
mult(plus(X1,X2),plus(X2,mult(X1,X2))) = X2,
inference(spm,[status(thm)],[c_0_9,c_0_11]) ).
cnf(c_0_13,plain,
plus(plus(mult(X1,mult(X1,X2)),mult(X3,X1)),X1) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,plain,
mult(plus(X1,X1),plus(X2,mult(X1,plus(plus(mult(X1,X3),mult(X4,X1)),X1)))) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_13]) ).
cnf(c_0_15,plain,
mult(plus(X1,mult(X2,X2)),plus(X2,mult(X1,mult(X2,X2)))) = X2,
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_16,plain,
mult(plus(X1,X1),plus(X2,mult(X1,X1))) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_17,plain,
mult(X1,plus(X1,mult(plus(mult(X1,mult(X1,X2)),mult(X3,X1)),X1))) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,plain,
mult(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
plus(plus(mult(X1,X1),mult(X2,X1)),X1) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_17]) ).
cnf(c_0_20,plain,
plus(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_18]),c_0_18]) ).
cnf(c_0_21,plain,
mult(X1,plus(X1,mult(plus(mult(X1,X1),mult(X2,X1)),X1))) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_17]) ).
cnf(c_0_22,plain,
plus(plus(X1,mult(X2,X1)),X1) = X1,
inference(rw,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_23,plain,
mult(X1,plus(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_18]),c_0_20]) ).
cnf(c_0_24,plain,
mult(plus(plus(X1,X2),plus(X1,mult(X1,X2))),plus(plus(X1,X2),X1)) = plus(X1,X2),
inference(spm,[status(thm)],[c_0_7,c_0_7]) ).
cnf(c_0_25,plain,
mult(X1,plus(X1,mult(plus(X1,mult(X2,X1)),X1))) = X1,
inference(rw,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_26,plain,
plus(X1,plus(X1,mult(X2,X1))) = plus(X1,mult(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_12]),c_0_22]) ).
cnf(c_0_27,plain,
mult(plus(X1,plus(X2,X1)),plus(plus(X2,X1),X1)) = plus(X2,X1),
inference(spm,[status(thm)],[c_0_12,c_0_23]) ).
cnf(c_0_28,plain,
mult(plus(X1,plus(plus(mult(X2,mult(X1,X3)),mult(X4,X1)),X1)),plus(X5,X1)) = X1,
inference(rw,[status(thm)],[c_0_11,c_0_23]) ).
cnf(c_0_29,plain,
plus(X1,mult(plus(X1,mult(X2,X1)),X1)) = X1,
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_20]),c_0_22]),c_0_26]),c_0_22]),c_0_18]),c_0_26]) ).
cnf(c_0_30,plain,
plus(plus(mult(X1,mult(X2,X3)),mult(X4,X2)),X2) = X2,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,plain,
mult(plus(mult(plus(X1,mult(X2,X1)),X1),X1),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_29]),c_0_29]) ).
cnf(c_0_32,plain,
plus(plus(X1,X2),mult(plus(plus(X1,X2),X2),plus(X1,X2))) = plus(X1,X2),
inference(spm,[status(thm)],[c_0_29,c_0_23]) ).
cnf(c_0_33,plain,
plus(plus(mult(X1,mult(X2,X3)),X2),X2) = X2,
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,plain,
plus(plus(mult(plus(X1,X2),X2),mult(X3,plus(X1,X2))),plus(X1,X2)) = plus(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_35,plain,
plus(mult(X1,mult(X2,X3)),X2) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_23]),c_0_33]) ).
cnf(c_0_36,plain,
mult(X1,plus(X1,mult(X1,mult(plus(X1,mult(X2,X1)),X1)))) = X1,
inference(spm,[status(thm)],[c_0_7,c_0_29]) ).
cnf(c_0_37,plain,
mult(plus(X1,plus(X2,X1)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_23]),c_0_20]) ).
cnf(c_0_38,plain,
plus(plus(mult(plus(X1,X2),X2),X2),plus(X1,X2)) = plus(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_23]) ).
cnf(c_0_39,plain,
plus(mult(X1,X2),X2) = X2,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
plus(mult(X1,X2),X1) = X1,
inference(spm,[status(thm)],[c_0_35,c_0_37]) ).
cnf(c_0_41,plain,
plus(mult(X1,X2),plus(X2,X3)) = plus(X2,X3),
inference(spm,[status(thm)],[c_0_35,c_0_7]) ).
cnf(c_0_42,plain,
plus(X1,plus(X2,X1)) = plus(X2,X1),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
mult(X1,plus(X1,mult(mult(X1,X2),X1))) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_40]) ).
cnf(c_0_44,plain,
plus(X1,plus(plus(X1,mult(X2,X1)),X3)) = plus(plus(X1,mult(X2,X1)),X3),
inference(spm,[status(thm)],[c_0_41,c_0_12]) ).
cnf(c_0_45,plain,
mult(plus(X1,X2),X2) = X2,
inference(rw,[status(thm)],[c_0_37,c_0_42]) ).
cnf(c_0_46,plain,
plus(X1,mult(mult(X1,X2),X1)) = X1,
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_43]),c_0_26]),c_0_20]),c_0_22]),c_0_26]),c_0_22]),c_0_18]),c_0_26]) ).
cnf(c_0_47,plain,
plus(plus(X1,mult(X2,X1)),plus(X1,X3)) = plus(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_12]),c_0_22]),c_0_22]) ).
cnf(c_0_48,plain,
mult(X1,mult(mult(X1,X2),X1)) = mult(mult(X1,X2),X1),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_49,plain,
mult(plus(X1,mult(X1,mult(X2,X1))),X1) = plus(X1,mult(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_47]),c_0_22]) ).
cnf(c_0_50,plain,
plus(X1,mult(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_7]),c_0_49]),c_0_7]) ).
cnf(c_0_51,plain,
mult(plus(X1,mult(mult(X2,plus(X2,X3)),X2)),plus(X2,mult(X1,mult(mult(X2,plus(X2,X3)),X2)))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_20]),c_0_20]) ).
cnf(c_0_52,plain,
mult(mult(X1,X2),X2) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_23,c_0_50]) ).
cnf(c_0_53,plain,
plus(X1,plus(X1,X2)) = plus(X1,X2),
inference(spm,[status(thm)],[c_0_40,c_0_7]) ).
cnf(c_0_54,plain,
mult(mult(X1,plus(X1,X2)),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_18]),c_0_20]),c_0_46]),c_0_52]) ).
cnf(c_0_55,plain,
mult(plus(plus(X1,X2),plus(X1,mult(X1,plus(X1,X2)))),plus(plus(X1,X2),X1)) = plus(X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_53]) ).
cnf(c_0_56,plain,
mult(X1,plus(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_54]),c_0_40]),c_0_40]),c_0_18]) ).
cnf(c_0_57,plain,
plus(plus(X1,X2),X1) = plus(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56]),c_0_20]),c_0_18]) ).
cnf(c_0_58,negated_conjecture,
plus(a,mult(b,mult(a,c))) != a,
goals ).
cnf(c_0_59,plain,
plus(X1,mult(X2,mult(X1,X3))) = X1,
inference(spm,[status(thm)],[c_0_57,c_0_35]) ).
cnf(c_0_60,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT390-1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n015.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 21:50:01 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 119.38/75.40 % Version : CSE_E---1.7
% 119.38/75.40 % Problem : theBenchmark.p
% 119.38/75.40 % SZS status Unsatisfiable for theBenchmark.p
% 119.38/75.40 % SZS output start CNFRefutation
% See solution above
% 119.78/75.81 % Total time : 60.515s
%------------------------------------------------------------------------------