%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP203-1 : 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 : n009.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 3.84s 3.25s
% Output : CNFRefutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of clauses : 43 ( 43 unt; 0 nHn; 3 RR)
% Number of literals : 43 ( 42 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 83 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
cnf(left_inverse,axiom,
multiply(left_inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
cnf(prove_moufang2,negated_conjecture,
multiply(multiply(multiply(a,b),c),b) != multiply(a,multiply(b,multiply(c,b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_moufang2) ).
cnf(c_0_4,axiom,
multiply(multiply(multiply(X1,X2),X1),X3) = multiply(X1,multiply(X2,multiply(X1,X3))),
moufang3 ).
cnf(c_0_5,axiom,
multiply(identity,X1) = X1,
left_identity ).
cnf(c_0_6,plain,
multiply(multiply(X1,identity),X2) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_5]),c_0_5]),c_0_5]) ).
cnf(c_0_7,axiom,
multiply(left_inverse(X1),X1) = identity,
left_inverse ).
cnf(c_0_8,plain,
multiply(multiply(X1,X1),X2) = multiply(X1,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_6]),c_0_5]) ).
cnf(c_0_9,plain,
multiply(left_inverse(X1),multiply(X1,multiply(left_inverse(X1),X2))) = multiply(left_inverse(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_7]),c_0_5]) ).
cnf(c_0_10,plain,
multiply(multiply(X1,multiply(X2,multiply(X1,identity))),X3) = multiply(X1,multiply(X2,multiply(X1,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_4]),c_0_4]) ).
cnf(c_0_11,plain,
multiply(multiply(X1,multiply(X1,identity)),X2) = multiply(X1,multiply(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_8]),c_0_8]) ).
cnf(c_0_12,plain,
multiply(left_inverse(X1),multiply(X1,identity)) = identity,
inference(spm,[status(thm)],[c_0_9,c_0_7]) ).
cnf(c_0_13,plain,
multiply(multiply(X1,multiply(X2,multiply(X2,multiply(X1,identity)))),X3) = multiply(X1,multiply(X2,multiply(X2,multiply(X1,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_11]) ).
cnf(c_0_14,plain,
multiply(X1,multiply(left_inverse(X1),multiply(X1,X2))) = multiply(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_12]),c_0_6]) ).
cnf(c_0_15,plain,
multiply(X1,multiply(left_inverse(X1),multiply(left_inverse(X1),multiply(X1,X2)))) = multiply(multiply(X1,multiply(left_inverse(X1),identity)),X2),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_16,plain,
multiply(left_inverse(X1),multiply(left_inverse(left_inverse(X1)),identity)) = identity,
inference(spm,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_17,plain,
multiply(left_inverse(X1),multiply(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_15]),c_0_16]),c_0_5]),c_0_16]),c_0_5]) ).
cnf(c_0_18,plain,
multiply(left_inverse(left_inverse(X1)),identity) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_7]) ).
cnf(c_0_19,plain,
multiply(left_inverse(left_inverse(X1)),X2) = multiply(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_17]) ).
cnf(c_0_20,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,plain,
left_inverse(left_inverse(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_20]) ).
cnf(c_0_22,plain,
multiply(multiply(X1,X2),X1) = multiply(X1,multiply(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_20]),c_0_20]) ).
cnf(c_0_23,plain,
multiply(X1,multiply(left_inverse(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
cnf(c_0_24,plain,
multiply(X1,multiply(multiply(left_inverse(X1),X2),X1)) = multiply(X2,X1),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,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_23,c_0_24]),c_0_21]) ).
cnf(c_0_26,plain,
multiply(multiply(X1,multiply(X2,X1)),X3) = multiply(X1,multiply(X2,multiply(X1,X3))),
inference(rw,[status(thm)],[c_0_10,c_0_20]) ).
cnf(c_0_27,plain,
multiply(X1,left_inverse(X1)) = identity,
inference(spm,[status(thm)],[c_0_7,c_0_21]) ).
cnf(c_0_28,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_25,c_0_26]),c_0_27]),c_0_20]) ).
cnf(c_0_29,plain,
multiply(multiply(X1,left_inverse(X2)),X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_28]),c_0_23]),c_0_21]) ).
cnf(c_0_30,plain,
multiply(multiply(X1,X2),left_inverse(X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_28]),c_0_17]) ).
cnf(c_0_31,plain,
multiply(multiply(X1,multiply(X2,multiply(X1,left_inverse(X3)))),X3) = multiply(X1,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_29,c_0_26]) ).
cnf(c_0_32,plain,
multiply(X1,left_inverse(multiply(X2,X1))) = left_inverse(X2),
inference(spm,[status(thm)],[c_0_30,c_0_17]) ).
cnf(c_0_33,plain,
multiply(multiply(left_inverse(X1),X2),X1) = multiply(left_inverse(X1),multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_24]) ).
cnf(c_0_34,plain,
multiply(multiply(X1,multiply(X2,left_inverse(X3))),multiply(X3,X1)) = multiply(X1,multiply(X2,X1)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
multiply(X1,multiply(multiply(X2,left_inverse(X1)),multiply(X1,X3))) = multiply(multiply(X1,X2),X3),
inference(spm,[status(thm)],[c_0_26,c_0_29]) ).
cnf(c_0_36,plain,
multiply(X1,multiply(multiply(left_inverse(X1),X2),multiply(X1,X3))) = multiply(multiply(X2,X1),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_33]),c_0_23]) ).
cnf(c_0_37,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_34,c_0_29]),c_0_21]) ).
cnf(c_0_38,plain,
multiply(multiply(X1,left_inverse(X2)),multiply(X2,X3)) = multiply(left_inverse(X2),multiply(multiply(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_17,c_0_35]) ).
cnf(c_0_39,plain,
multiply(multiply(X1,X2),multiply(left_inverse(X1),X3)) = multiply(X1,multiply(multiply(X2,left_inverse(X1)),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_36]),c_0_21]) ).
cnf(c_0_40,negated_conjecture,
multiply(multiply(multiply(a,b),c),b) != multiply(a,multiply(b,multiply(c,b))),
prove_moufang2 ).
cnf(c_0_41,plain,
multiply(multiply(multiply(X1,X2),X3),X2) = multiply(X1,multiply(X2,multiply(X3,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_17]),c_0_38]),c_0_39]),c_0_37]),c_0_17]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP203-1 : TPTP v9.2.1. Released v2.2.0.
% 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
% 0.16/0.33 % Computer : n009.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:29:11 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 3.84/3.25 % Version : CSE_E---1.7
% 3.84/3.25 % Problem : theBenchmark.p
% 3.84/3.25 % SZS status Unsatisfiable for theBenchmark.p
% 3.84/3.25 % SZS output start CNFRefutation
% See solution above
% 3.84/3.26 % Total time : 2.370s
%------------------------------------------------------------------------------