%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP748-5 : 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 : n031.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 04:27:12 PM UTC 2026
% Result : Unsatisfiable 3.50s 3.07s
% Output : CNFRefutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of clauses : 36 ( 30 unt; 4 nHn; 5 RR)
% Number of literals : 42 ( 41 equ; 4 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f11,axiom,
( mult(X1,X2) = mult(X2,X1)
| mult(i(X1),mult(X1,X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f11) ).
cnf(f01,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
cnf(f08,axiom,
mult(mult(X1,X2),i(X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).
cnf(f07,axiom,
mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(mult(X2,X3),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
cnf(f10,axiom,
mult(i(X1),X1) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f10) ).
cnf(f06,axiom,
mult(unit,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
cnf(f09,axiom,
mult(X1,i(X1)) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f09) ).
cnf(f02,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
cnf(goals,negated_conjecture,
mult(mult(a,b),mult(c,a)) != mult(a,mult(mult(b,c),a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c_0_9,axiom,
( mult(X1,X2) = mult(X2,X1)
| mult(i(X1),mult(X1,X2)) = X2 ),
f11 ).
cnf(c_0_10,axiom,
mult(X1,ld(X1,X2)) = X2,
f01 ).
cnf(c_0_11,axiom,
mult(mult(X1,X2),i(X2)) = X1,
f08 ).
cnf(c_0_12,plain,
( ld(X1,X2) = mult(i(X1),X2)
| mult(ld(X1,X2),X1) = X2 ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
( ld(X1,X2) = mult(i(X1),X2)
| ld(X1,X2) = mult(X2,i(X1)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,axiom,
mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(mult(X2,X3),X2)),
f07 ).
cnf(c_0_15,axiom,
mult(i(X1),X1) = unit,
f10 ).
cnf(c_0_16,axiom,
mult(unit,X1) = X1,
f06 ).
cnf(c_0_17,plain,
( ld(X1,X2) = mult(X2,i(X1))
| mult(i(X1),X2) != mult(X2,i(X1)) ),
inference(ef,[status(thm)],[c_0_13]) ).
cnf(c_0_18,axiom,
mult(X1,i(X1)) = unit,
f09 ).
cnf(c_0_19,axiom,
ld(X1,mult(X1,X2)) = X2,
f02 ).
cnf(c_0_20,plain,
mult(i(X1),mult(mult(X1,X2),X1)) = mult(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_21,plain,
( mult(X1,mult(X2,i(X1))) = X2
| mult(i(X1),X2) != mult(X2,i(X1)) ),
inference(spm,[status(thm)],[c_0_10,c_0_17]) ).
cnf(c_0_22,plain,
i(i(X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_18]),c_0_16]) ).
cnf(c_0_23,plain,
ld(i(X1),mult(X2,X1)) = mult(mult(X1,X2),X1),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
ld(i(X1),X2) = mult(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_12]),c_0_22]),c_0_10])]) ).
cnf(c_0_25,plain,
mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,plain,
mult(i(X1),mult(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_10,c_0_24]) ).
cnf(c_0_27,plain,
mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(X2,mult(X3,X2))),
inference(rw,[status(thm)],[c_0_14,c_0_25]) ).
cnf(c_0_28,plain,
mult(mult(X1,i(X2)),X2) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_22]) ).
cnf(c_0_29,plain,
mult(X1,i(mult(X2,X1))) = i(X2),
inference(spm,[status(thm)],[c_0_11,c_0_26]) ).
cnf(c_0_30,plain,
mult(mult(X1,i(X2)),mult(X2,mult(X3,X2))) = mult(mult(X1,X3),X2),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,plain,
i(mult(X1,X2)) = mult(i(X2),i(X1)),
inference(spm,[status(thm)],[c_0_26,c_0_29]) ).
cnf(c_0_32,plain,
mult(mult(X1,i(X2)),mult(mult(X2,X3),X1)) = mult(X1,mult(X3,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_30]),c_0_31]),c_0_22]) ).
cnf(c_0_33,negated_conjecture,
mult(mult(a,b),mult(c,a)) != mult(a,mult(mult(b,c),a)),
goals ).
cnf(c_0_34,plain,
mult(mult(X1,X2),mult(X3,X1)) = mult(X1,mult(mult(X2,X3),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_26]),c_0_22]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP748-5 : 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 : n031.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 19:06:53 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 3.50/3.07 % Version : CSE_E---1.7
% 3.50/3.07 % Problem : theBenchmark.p
% 3.50/3.07 % SZS status Unsatisfiable for theBenchmark.p
% 3.50/3.07 % SZS output start CNFRefutation
% See solution above
% 3.50/3.08 % Total time : 2.372s
%------------------------------------------------------------------------------