%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP205-1 : TPTP v9.2.1. Released v2.3.0.
% 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 : n020.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 4.37s 3.32s
% Output : CNFRefutation 4.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of clauses : 49 ( 49 unt; 0 nHn; 3 RR)
% Number of literals : 49 ( 48 equ; 2 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 86 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(right_identity,axiom,
multiply(X1,identity) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).
cnf(moufang3,axiom,
multiply(multiply(multiply(X1,X2),X1),X3) = multiply(X1,multiply(X2,multiply(X1,X3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',moufang3) ).
cnf(left_inverse,axiom,
multiply(left_inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
cnf(right_inverse,axiom,
multiply(X1,right_inverse(X1)) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
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(right_division_multiply,axiom,
right_division(multiply(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_division_multiply) ).
cnf(multiply_right_division,axiom,
multiply(right_division(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_right_division) ).
cnf(prove_moufang4,negated_conjecture,
multiply(x,multiply(multiply(y,z),x)) != multiply(multiply(x,y),multiply(z,x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_moufang4) ).
cnf(c_0_10,axiom,
multiply(X1,identity) = X1,
right_identity ).
cnf(c_0_11,axiom,
multiply(multiply(multiply(X1,X2),X1),X3) = multiply(X1,multiply(X2,multiply(X1,X3))),
moufang3 ).
cnf(c_0_12,plain,
multiply(multiply(X1,X2),X1) = multiply(X1,multiply(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_10]) ).
cnf(c_0_13,plain,
multiply(multiply(X1,multiply(X2,X1)),X3) = multiply(X1,multiply(X2,multiply(X1,X3))),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,axiom,
multiply(left_inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_15,axiom,
multiply(X1,right_inverse(X1)) = identity,
right_inverse ).
cnf(c_0_16,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_17,axiom,
left_division(X1,multiply(X1,X2)) = X2,
left_division_multiply ).
cnf(c_0_18,axiom,
multiply(X1,left_division(X1,X2)) = X2,
multiply_left_division ).
cnf(c_0_19,plain,
multiply(X1,multiply(left_inverse(X1),multiply(X1,X2))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_10]) ).
cnf(c_0_20,plain,
multiply(X1,multiply(right_inverse(X1),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_15]),c_0_16]) ).
cnf(c_0_21,plain,
left_division(X1,X1) = identity,
inference(spm,[status(thm)],[c_0_17,c_0_10]) ).
cnf(c_0_22,axiom,
right_division(multiply(X1,X2),X2) = X1,
right_division_multiply ).
cnf(c_0_23,plain,
multiply(X1,multiply(left_division(X1,X2),X1)) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_12,c_0_18]) ).
cnf(c_0_24,plain,
multiply(left_inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_19]),c_0_17]) ).
cnf(c_0_25,plain,
multiply(right_inverse(X1),X1) = identity,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_20]),c_0_21]) ).
cnf(c_0_26,plain,
right_division(identity,X1) = left_inverse(X1),
inference(spm,[status(thm)],[c_0_22,c_0_14]) ).
cnf(c_0_27,plain,
multiply(left_division(X1,X2),X1) = left_division(X1,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_28,plain,
left_division(left_inverse(X1),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
cnf(c_0_29,plain,
right_inverse(X1) = left_inverse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_25]),c_0_26]) ).
cnf(c_0_30,plain,
multiply(multiply(X1,X2),left_inverse(X1)) = multiply(X1,multiply(X2,left_inverse(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_28]) ).
cnf(c_0_31,plain,
multiply(X1,left_inverse(X1)) = identity,
inference(rw,[status(thm)],[c_0_15,c_0_29]) ).
cnf(c_0_32,plain,
right_division(X1,left_division(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_33,plain,
multiply(X1,multiply(multiply(X2,X1),left_inverse(X1))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_30]),c_0_31]),c_0_10]) ).
cnf(c_0_34,plain,
right_division(X1,multiply(X2,X1)) = left_inverse(X2),
inference(spm,[status(thm)],[c_0_32,c_0_28]) ).
cnf(c_0_35,axiom,
multiply(right_division(X1,X2),X2) = X1,
multiply_right_division ).
cnf(c_0_36,plain,
multiply(multiply(X1,X2),left_inverse(X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_33]),c_0_17]) ).
cnf(c_0_37,plain,
left_inverse(right_division(X1,X2)) = right_division(X2,X1),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
right_division(X1,left_inverse(X2)) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_36]) ).
cnf(c_0_39,plain,
right_division(left_inverse(X1),X2) = left_inverse(multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,plain,
multiply(left_inverse(X1),X2) = left_division(X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_18]) ).
cnf(c_0_41,plain,
left_inverse(left_division(X1,X2)) = left_division(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_40]) ).
cnf(c_0_42,plain,
right_division(multiply(X1,multiply(X2,multiply(X1,X3))),X3) = multiply(X1,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_22,c_0_13]) ).
cnf(c_0_43,plain,
right_division(X1,left_division(X2,X3)) = multiply(X1,left_division(X3,X2)),
inference(spm,[status(thm)],[c_0_38,c_0_41]) ).
cnf(c_0_44,plain,
multiply(multiply(X1,multiply(X2,X3)),left_division(X3,X1)) = multiply(X1,multiply(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_18]),c_0_43]) ).
cnf(c_0_45,plain,
multiply(multiply(X1,X2),left_division(X3,X1)) = multiply(X1,multiply(right_division(X2,X3),X1)),
inference(spm,[status(thm)],[c_0_44,c_0_35]) ).
cnf(c_0_46,negated_conjecture,
multiply(x,multiply(multiply(y,z),x)) != multiply(multiply(x,y),multiply(z,x)),
prove_moufang4 ).
cnf(c_0_47,plain,
multiply(multiply(X1,X2),multiply(X3,X1)) = multiply(X1,multiply(multiply(X2,X3),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_28]),c_0_38]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP205-1 : TPTP v9.2.1. Released v2.3.0.
% 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
% 0.15/0.33 % Computer : n020.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 18:29:20 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 4.37/3.32 % Version : CSE_E---1.7
% 4.37/3.32 % Problem : theBenchmark.p
% 4.37/3.32 % SZS status Unsatisfiable for theBenchmark.p
% 4.37/3.32 % SZS output start CNFRefutation
% See solution above
% 4.37/3.33 % Total time : 2.372s
%------------------------------------------------------------------------------