%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP201-1 : TPTP v9.2.1. Released v2.2.0.
% 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 : n023.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 04:24:48 PM UTC 2026
% Result : Unsatisfiable 1.84s 2.18s
% Output : CNFRefutation 1.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of clauses : 45 ( 45 unt; 0 nHn; 4 RR)
% Number of literals : 45 ( 44 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(right_division_multiply,axiom,
right_division(multiply(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_division_multiply) ).
cnf(moufang2,axiom,
multiply(multiply(multiply(X1,X2),X3),X2) = multiply(X1,multiply(X2,multiply(X3,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',moufang2) ).
cnf(left_inverse,axiom,
multiply(left_inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
cnf(right_identity,axiom,
multiply(X1,identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
cnf(multiply_right_division,axiom,
multiply(right_division(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_right_division) ).
cnf(left_division_multiply,axiom,
left_division(X1,multiply(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_division_multiply) ).
cnf(multiply_left_division,axiom,
multiply(X1,left_division(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_left_division) ).
cnf(prove_moufang3,negated_conjecture,
multiply(multiply(multiply(a,b),a),c) != multiply(a,multiply(b,multiply(a,c))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_moufang3) ).
cnf(c_0_9,axiom,
right_division(multiply(X1,X2),X2) = X1,
right_division_multiply ).
cnf(c_0_10,axiom,
multiply(multiply(multiply(X1,X2),X3),X2) = multiply(X1,multiply(X2,multiply(X3,X2))),
moufang2 ).
cnf(c_0_11,plain,
right_division(multiply(X1,multiply(X2,multiply(X3,X2))),X2) = multiply(multiply(X1,X2),X3),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,axiom,
multiply(left_inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_13,axiom,
multiply(X1,identity) = X1,
right_identity ).
cnf(c_0_14,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_15,plain,
multiply(multiply(X1,X2),left_inverse(X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_9]) ).
cnf(c_0_16,axiom,
multiply(right_division(X1,X2),X2) = X1,
multiply_right_division ).
cnf(c_0_17,axiom,
left_division(X1,multiply(X1,X2)) = X2,
left_division_multiply ).
cnf(c_0_18,plain,
multiply(multiply(X1,X2),X1) = multiply(X1,multiply(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_14]),c_0_14]) ).
cnf(c_0_19,plain,
multiply(X1,left_inverse(X2)) = right_division(X1,X2),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
left_division(right_division(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_21,plain,
right_division(X1,left_inverse(X2)) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_9,c_0_15]) ).
cnf(c_0_22,plain,
multiply(left_inverse(X1),right_division(X2,X1)) = right_division(multiply(left_inverse(X1),X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_19]) ).
cnf(c_0_23,plain,
right_division(multiply(X1,multiply(X2,X1)),X1) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_9,c_0_18]) ).
cnf(c_0_24,plain,
left_division(multiply(X1,X2),X1) = left_inverse(X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,axiom,
multiply(X1,left_division(X1,X2)) = X2,
multiply_left_division ).
cnf(c_0_26,plain,
multiply(left_inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_11]),c_0_12]),c_0_14]) ).
cnf(c_0_27,plain,
multiply(X1,right_division(X2,X1)) = right_division(multiply(X1,X2),X1),
inference(spm,[status(thm)],[c_0_23,c_0_16]) ).
cnf(c_0_28,plain,
left_inverse(left_division(X1,X2)) = left_division(X2,X1),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
left_division(left_inverse(X1),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_26]) ).
cnf(c_0_30,plain,
multiply(left_inverse(X1),X2) = left_division(X1,X2),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_31,plain,
left_division(X1,right_division(multiply(X1,X2),X1)) = right_division(X2,X1),
inference(spm,[status(thm)],[c_0_17,c_0_27]) ).
cnf(c_0_32,plain,
left_division(X1,left_inverse(X2)) = left_inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
multiply(multiply(left_division(X1,X2),X3),X2) = left_division(X1,multiply(X2,multiply(X3,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_30]),c_0_30]) ).
cnf(c_0_34,plain,
right_division(left_division(X1,X2),X1) = left_division(X1,right_division(X2,X1)),
inference(spm,[status(thm)],[c_0_31,c_0_25]) ).
cnf(c_0_35,plain,
left_inverse(right_division(X1,X2)) = right_division(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_32]),c_0_19]),c_0_19]) ).
cnf(c_0_36,plain,
left_division(X1,left_division(X2,right_division(X3,X2))) = right_division(left_division(multiply(X2,X1),X3),X2),
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_19,c_0_33]),c_0_19]),c_0_22]),c_0_30]),c_0_34]),c_0_32]),c_0_30]) ).
cnf(c_0_37,plain,
right_division(X1,left_division(X2,X3)) = multiply(X1,left_division(X3,X2)),
inference(spm,[status(thm)],[c_0_21,c_0_28]) ).
cnf(c_0_38,plain,
left_division(left_division(X1,X2),X3) = multiply(left_division(X2,X1),X3),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_39,plain,
left_division(right_division(X1,X2),X3) = multiply(right_division(X2,X1),X3),
inference(spm,[status(thm)],[c_0_29,c_0_35]) ).
cnf(c_0_40,negated_conjecture,
multiply(multiply(multiply(a,b),a),c) != multiply(a,multiply(b,multiply(a,c))),
prove_moufang3 ).
cnf(c_0_41,plain,
multiply(X1,left_division(X2,multiply(X1,X3))) = multiply(multiply(right_division(X1,X2),X1),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_36]),c_0_35]),c_0_37]),c_0_38]),c_0_39]) ).
cnf(c_0_42,negated_conjecture,
multiply(multiply(a,multiply(b,a)),c) != multiply(a,multiply(b,multiply(a,c))),
inference(rw,[status(thm)],[c_0_40,c_0_18]) ).
cnf(c_0_43,plain,
multiply(multiply(X1,multiply(X2,X1)),X3) = multiply(X1,multiply(X2,multiply(X1,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_29]),c_0_21]),c_0_18]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.21 % Problem : GRP201-1 : TPTP v9.2.1. Released v2.2.0.
% 0.02/0.21 % 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
% 0.13/0.44 % Computer : n023.cluster.edu
% 0.13/0.44 % Model : x86_64 x86_64
% 0.13/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.44 % Memory : 8042.1875MB
% 0.13/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.44 % CPULimit : 300
% 0.13/0.44 % WCLimit : 300
% 0.13/0.44 % DateTime : Mon May 4 18:30:08 EDT 2026
% 0.15/0.45 % CPUTime :
% 0.15/0.46 % start to proof: theBenchmark
% 1.84/2.18 % Version : CSE_E---1.7
% 1.84/2.18 % Problem : theBenchmark.p
% 1.84/2.18 % SZS status Unsatisfiable for theBenchmark.p
% 1.84/2.18 % SZS output start CNFRefutation
% See solution above
% 1.84/2.19 % Total time : 1.382s
%------------------------------------------------------------------------------