%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP470-1 : TPTP v9.2.1. Released v2.6.0.
% 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 : n017.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 04:26:11 PM UTC 2026
% Result : Unsatisfiable 3.37s 3.10s
% Output : CNFRefutation 3.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 3
% Syntax : Number of clauses : 63 ( 63 unt; 0 nHn; 5 RR)
% Number of literals : 63 ( 62 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 186 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(single_axiom,axiom,
divide(inverse(divide(X1,divide(X2,divide(X3,X4)))),divide(divide(X4,X3),X1)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
cnf(prove_these_axioms_2,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).
cnf(multiply,axiom,
multiply(X1,X2) = divide(X1,inverse(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
cnf(c_0_3,axiom,
divide(inverse(divide(X1,divide(X2,divide(X3,X4)))),divide(divide(X4,X3),X1)) = X2,
single_axiom ).
cnf(c_0_4,plain,
divide(inverse(divide(X1,X2)),divide(divide(X3,divide(X4,X5)),X1)) = inverse(divide(X3,divide(X2,divide(X5,X4)))),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_5,plain,
inverse(divide(X1,divide(divide(X2,divide(divide(X3,X4),X1)),divide(X4,X3)))) = X2,
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_6,plain,
divide(inverse(X1),divide(divide(X2,X3),inverse(divide(divide(X3,X2),divide(X1,divide(X4,X5)))))) = divide(X5,X4),
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_7,plain,
inverse(inverse(divide(X1,divide(X2,divide(inverse(divide(divide(X3,X4),X2)),divide(X4,X3)))))) = X1,
inference(spm,[status(thm)],[c_0_5,c_0_4]) ).
cnf(c_0_8,plain,
divide(divide(divide(X1,X2),inverse(divide(divide(X2,X1),divide(X3,divide(X4,X5))))),inverse(X3)) = divide(X4,X5),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_6]),c_0_6]) ).
cnf(c_0_9,plain,
divide(inverse(divide(X1,divide(X2,divide(divide(divide(X3,X4),X5),inverse(divide(X5,divide(X6,divide(X4,X3)))))))),divide(X6,X1)) = X2,
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_10,plain,
inverse(divide(divide(inverse(divide(divide(X1,X2),divide(X3,X4))),divide(X2,X1)),divide(X5,divide(X4,X3)))) = inverse(inverse(X5)),
inference(spm,[status(thm)],[c_0_7,c_0_3]) ).
cnf(c_0_11,plain,
divide(divide(divide(X1,X2),inverse(divide(divide(X2,X1),divide(X3,X4)))),inverse(X3)) = X4,
inference(spm,[status(thm)],[c_0_8,c_0_3]) ).
cnf(c_0_12,plain,
divide(inverse(divide(X1,divide(X2,X3))),divide(divide(divide(divide(X4,X5),X6),inverse(divide(X6,divide(X3,divide(X5,X4))))),X1)) = X2,
inference(spm,[status(thm)],[c_0_3,c_0_3]) ).
cnf(c_0_13,plain,
divide(inverse(inverse(X1)),divide(X2,divide(inverse(divide(divide(X3,X4),X2)),divide(X4,X3)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_3]) ).
cnf(c_0_14,plain,
divide(divide(divide(X1,X2),X3),inverse(divide(X3,divide(divide(X4,X5),divide(X2,X1))))) = divide(X5,X4),
inference(spm,[status(thm)],[c_0_11,c_0_5]) ).
cnf(c_0_15,plain,
divide(inverse(X1),divide(divide(divide(X2,X3),inverse(divide(divide(X3,X2),X4))),inverse(inverse(X1)))) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_16,plain,
divide(X1,divide(divide(divide(X2,X3),inverse(divide(divide(X3,X2),X4))),inverse(X1))) = X4,
inference(spm,[status(thm)],[c_0_15,c_0_7]) ).
cnf(c_0_17,plain,
divide(divide(divide(X1,X2),inverse(X3)),inverse(divide(divide(X4,X5),inverse(divide(divide(X5,X4),X3))))) = inverse(divide(X2,X1)),
inference(spm,[status(thm)],[c_0_11,c_0_16]) ).
cnf(c_0_18,plain,
divide(X1,divide(inverse(divide(X2,X3)),inverse(X1))) = inverse(divide(divide(divide(X3,X2),inverse(X4)),X4)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,plain,
divide(X1,divide(inverse(divide(X2,X3)),inverse(X1))) = divide(X4,divide(inverse(divide(X2,X3)),inverse(X4))),
inference(spm,[status(thm)],[c_0_18,c_0_18]) ).
cnf(c_0_20,plain,
inverse(divide(inverse(X1),divide(divide(X2,X3),divide(inverse(divide(divide(X4,X5),divide(X1,X3))),divide(X5,X4))))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_11]),c_0_4]) ).
cnf(c_0_21,plain,
divide(X1,divide(X2,inverse(X1))) = divide(X3,divide(X2,inverse(X3))),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,plain,
inverse(divide(X1,divide(divide(X2,divide(divide(X3,inverse(X4)),X4)),divide(inverse(X1),X3)))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_3,c_0_21]),c_0_4]) ).
cnf(c_0_23,plain,
divide(divide(X1,X2),divide(X3,divide(divide(divide(X2,X1),inverse(X4)),X4))) = inverse(X3),
inference(spm,[status(thm)],[c_0_7,c_0_22]) ).
cnf(c_0_24,plain,
inverse(inverse(divide(X1,divide(X2,divide(inverse(X1),divide(X3,X4)))))) = divide(divide(X4,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_9]),c_0_14]) ).
cnf(c_0_25,plain,
divide(divide(divide(X1,X2),inverse(divide(divide(X2,X1),inverse(X3)))),inverse(inverse(X4))) = inverse(inverse(divide(X3,X4))),
inference(spm,[status(thm)],[c_0_24,c_0_13]) ).
cnf(c_0_26,plain,
divide(inverse(X1),inverse(inverse(divide(X2,X1)))) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_25]),c_0_16]) ).
cnf(c_0_27,plain,
divide(X1,divide(inverse(X2),inverse(X1))) = divide(inverse(divide(X3,X2)),inverse(X3)),
inference(spm,[status(thm)],[c_0_21,c_0_26]) ).
cnf(c_0_28,plain,
divide(inverse(divide(X1,X2)),inverse(X1)) = divide(inverse(divide(X3,X2)),inverse(X3)),
inference(spm,[status(thm)],[c_0_27,c_0_27]) ).
cnf(c_0_29,plain,
divide(inverse(inverse(X1)),inverse(inverse(divide(inverse(divide(X2,X3)),inverse(X2))))) = inverse(inverse(divide(X1,X3))),
inference(spm,[status(thm)],[c_0_26,c_0_28]) ).
cnf(c_0_30,plain,
inverse(divide(inverse(X1),divide(X2,divide(inverse(divide(divide(X3,X4),X2)),divide(X4,X3))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_16]),c_0_14]),c_0_4]) ).
cnf(c_0_31,plain,
divide(inverse(inverse(X1)),inverse(inverse(divide(X2,inverse(inverse(X2)))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_7]) ).
cnf(c_0_32,plain,
divide(divide(divide(divide(X1,X2),inverse(divide(divide(X2,X1),divide(X3,X4)))),inverse(X5)),X5) = divide(X4,X3),
inference(spm,[status(thm)],[c_0_14,c_0_30]) ).
cnf(c_0_33,plain,
inverse(inverse(divide(X1,inverse(inverse(divide(X2,inverse(inverse(X2)))))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_31]),c_0_31]) ).
cnf(c_0_34,plain,
divide(divide(X1,inverse(X2)),X2) = divide(divide(X1,inverse(X3)),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_21]),c_0_32]) ).
cnf(c_0_35,plain,
divide(inverse(inverse(X1)),divide(X2,inverse(inverse(X2)))) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_33]) ).
cnf(c_0_36,plain,
divide(inverse(X1),inverse(inverse(divide(divide(X2,inverse(X3)),X3)))) = inverse(divide(X2,inverse(X1))),
inference(spm,[status(thm)],[c_0_26,c_0_34]) ).
cnf(c_0_37,plain,
divide(X1,divide(inverse(X2),inverse(X1))) = X2,
inference(spm,[status(thm)],[c_0_21,c_0_35]) ).
cnf(c_0_38,plain,
divide(X1,inverse(inverse(divide(divide(X2,inverse(X3)),X3)))) = inverse(divide(X2,X1)),
inference(spm,[status(thm)],[c_0_36,c_0_7]) ).
cnf(c_0_39,plain,
divide(inverse(divide(X1,inverse(inverse(X1)))),X2) = inverse(X2),
inference(spm,[status(thm)],[c_0_37,c_0_31]) ).
cnf(c_0_40,plain,
divide(inverse(inverse(inverse(divide(X1,X2)))),inverse(inverse(inverse(X1)))) = inverse(inverse(X2)),
inference(spm,[status(thm)],[c_0_26,c_0_26]) ).
cnf(c_0_41,plain,
inverse(inverse(divide(X1,divide(X2,inverse(inverse(X2)))))) = X1,
inference(spm,[status(thm)],[c_0_33,c_0_33]) ).
cnf(c_0_42,plain,
divide(X1,inverse(inverse(divide(inverse(inverse(X2)),X2)))) = inverse(inverse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_39]) ).
cnf(c_0_43,plain,
divide(inverse(divide(X1,inverse(inverse(divide(X2,X3))))),inverse(X1)) = divide(inverse(inverse(X2)),inverse(inverse(X3))),
inference(spm,[status(thm)],[c_0_27,c_0_40]) ).
cnf(c_0_44,plain,
divide(inverse(divide(X1,X2)),inverse(X1)) = X2,
inference(spm,[status(thm)],[c_0_27,c_0_35]) ).
cnf(c_0_45,plain,
inverse(inverse(inverse(inverse(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_42]) ).
cnf(c_0_46,plain,
divide(inverse(inverse(X1)),inverse(inverse(X2))) = inverse(inverse(divide(X1,X2))),
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,plain,
divide(X1,divide(X2,inverse(inverse(X2)))) = inverse(inverse(X1)),
inference(spm,[status(thm)],[c_0_35,c_0_45]) ).
cnf(c_0_48,plain,
inverse(inverse(divide(X1,divide(X2,inverse(X1))))) = inverse(X2),
inference(spm,[status(thm)],[c_0_26,c_0_46]) ).
cnf(c_0_49,plain,
inverse(inverse(divide(X1,divide(X2,divide(X3,divide(X4,inverse(X3))))))) = divide(divide(inverse(inverse(X1)),X4),X2),
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_50,plain,
divide(X1,divide(inverse(inverse(X2)),X2)) = inverse(inverse(X1)),
inference(spm,[status(thm)],[c_0_47,c_0_45]) ).
cnf(c_0_51,plain,
inverse(divide(X1,divide(X2,inverse(X1)))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_48]),c_0_37]) ).
cnf(c_0_52,plain,
divide(divide(inverse(inverse(X1)),X2),inverse(X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_45]),c_0_51]) ).
cnf(c_0_53,plain,
divide(inverse(inverse(X1)),X2) = inverse(divide(X2,X1)),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_54,plain,
inverse(divide(X1,divide(X2,X2))) = inverse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_53]),c_0_45]),c_0_53]) ).
cnf(c_0_55,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
prove_these_axioms_2 ).
cnf(c_0_56,axiom,
multiply(X1,X2) = divide(X1,inverse(X2)),
multiply ).
cnf(c_0_57,plain,
divide(X1,divide(X2,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_54]),c_0_37]) ).
cnf(c_0_58,negated_conjecture,
divide(divide(inverse(b2),inverse(b2)),inverse(a2)) != a2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56]),c_0_56]) ).
cnf(c_0_59,plain,
divide(divide(X1,X1),X2) = inverse(X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_57]),c_0_51]) ).
cnf(c_0_60,negated_conjecture,
inverse(inverse(a2)) != a2,
inference(rw,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_61,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_59]),c_0_57]),c_0_44]),c_0_57]) ).
cnf(c_0_62,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP470-1 : TPTP v9.2.1. Released v2.6.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n017.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 18:34:58 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 3.37/3.10 % Version : CSE_E---1.7
% 3.37/3.10 % Problem : theBenchmark.p
% 3.37/3.10 % SZS status Unsatisfiable for theBenchmark.p
% 3.37/3.10 % SZS output start CNFRefutation
% See solution above
% 3.37/3.10 % Total time : 2.372s
%------------------------------------------------------------------------------