%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP772-1 : TPTP v9.2.1. Released v4.1.0.
% 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 04:27:15 PM UTC 2026
% Result : Unsatisfiable 1.66s 1.88s
% Output : CNFRefutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 3 RR)
% Number of literals : 35 ( 34 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; 3 con; 0-3 aty)
% Number of variables : 73 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sos04,axiom,
difference(X1,product(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
cnf(sos29,axiom,
product(a(X1,X2,X3),difference(X3,product(a(X3,X1,X2),X3))) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos29) ).
cnf(sos03,axiom,
product(X1,difference(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
cnf(sos32,axiom,
a(j(X1),X2,X3) = a(X2,X3,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos32) ).
cnf(sos10,axiom,
j(X1) = quotient(one,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
cnf(sos31,axiom,
a(i(X1),X2,X3) = a(j(X1),X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos31) ).
cnf(sos09,axiom,
i(X1) = difference(X1,one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
cnf(sos06,axiom,
product(quotient(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
cnf(sos05,axiom,
quotient(product(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
cnf(goals,negated_conjecture,
a(x0,x1,x1) != a(x1,x1,x0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c_0_10,axiom,
difference(X1,product(X1,X2)) = X2,
sos04 ).
cnf(c_0_11,axiom,
product(a(X1,X2,X3),difference(X3,product(a(X3,X1,X2),X3))) = one,
sos29 ).
cnf(c_0_12,axiom,
product(X1,difference(X1,X2)) = X2,
sos03 ).
cnf(c_0_13,plain,
difference(X1,product(a(X1,X2,X3),X1)) = difference(a(X2,X3,X1),one),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,axiom,
a(j(X1),X2,X3) = a(X2,X3,X1),
sos32 ).
cnf(c_0_15,axiom,
j(X1) = quotient(one,X1),
sos10 ).
cnf(c_0_16,axiom,
a(i(X1),X2,X3) = a(j(X1),X2,X3),
sos31 ).
cnf(c_0_17,axiom,
i(X1) = difference(X1,one),
sos09 ).
cnf(c_0_18,plain,
product(X1,difference(a(X2,X3,X1),one)) = product(a(X1,X2,X3),X1),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
a(quotient(one,X1),X2,X3) = a(X2,X3,X1),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
a(quotient(one,X1),X2,X3) = a(difference(X1,one),X2,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_15]) ).
cnf(c_0_21,axiom,
product(quotient(X1,X2),X2) = X1,
sos06 ).
cnf(c_0_22,plain,
product(X1,difference(a(X2,X1,X3),one)) = product(a(X1,quotient(one,X3),X2),X1),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
a(difference(X1,one),X2,X3) = a(X2,X3,X1),
inference(rw,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_24,plain,
difference(quotient(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_10,c_0_21]) ).
cnf(c_0_25,axiom,
quotient(product(X1,X2),X2) = X1,
sos05 ).
cnf(c_0_26,plain,
product(a(X1,quotient(one,X1),X2),X1) = product(a(X1,X2,X1),X1),
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_27,plain,
a(X1,X2,quotient(one,X3)) = a(X3,X1,X2),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
a(X1,quotient(one,X1),X2) = a(X1,X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_25]) ).
cnf(c_0_29,plain,
a(X1,quotient(one,X2),X1) = a(X1,X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_27]) ).
cnf(c_0_30,plain,
quotient(X1,difference(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_25,c_0_12]) ).
cnf(c_0_31,plain,
difference(a(X1,X2,X2),one) = difference(a(X2,X2,X1),one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_29]),c_0_13]),c_0_19]) ).
cnf(c_0_32,negated_conjecture,
a(x0,x1,x1) != a(x1,x1,x0),
goals ).
cnf(c_0_33,plain,
a(X1,X2,X2) = a(X2,X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_30]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GRP772-1 : TPTP v9.2.1. Released v4.1.0.
% 0.11/0.13 % 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
% 0.17/0.34 % Computer : n020.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon May 4 19:05:50 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.20/0.35 % start to proof: theBenchmark
% 1.66/1.88 % Version : CSE_E---1.7
% 1.66/1.88 % Problem : theBenchmark.p
% 1.66/1.88 % SZS status Unsatisfiable for theBenchmark.p
% 1.66/1.88 % SZS output start CNFRefutation
% See solution above
% 1.66/1.88 % Total time : 1.371s
%------------------------------------------------------------------------------