%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG011-1 : TPTP v9.2.1. Released v2.7.0.
% 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 : n014.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 04:03:59 PM UTC 2026
% Result : Unsatisfiable 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of clauses : 25 ( 8 unt; 2 nHn; 21 RR)
% Number of literals : 58 ( 2 equ; 39 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(partitions_exclusive,hypothesis,
( ~ c(X1)
| ~ d(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_exclusive) ).
cnf(conjecture_1,negated_conjecture,
( d(f(X1,X2))
| ~ c(X1)
| ~ c(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_1) ).
cnf(conjecture_2,negated_conjecture,
( c(f(X1,X2))
| ~ d(X1)
| ~ d(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_2) ).
cnf(f_is_associative,axiom,
f(X1,f(X2,X3)) = f(f(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_is_associative) ).
cnf(partitions_union,axiom,
( c(X1)
| d(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_union) ).
cnf(partition_d_not_empty,hypothesis,
d(a2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partition_d_not_empty) ).
cnf(partition_c_not_empty,hypothesis,
c(a1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partition_c_not_empty) ).
cnf(c_0_7,hypothesis,
( ~ c(X1)
| ~ d(X1) ),
partitions_exclusive ).
cnf(c_0_8,negated_conjecture,
( d(f(X1,X2))
| ~ c(X1)
| ~ c(X2) ),
conjecture_1 ).
cnf(c_0_9,negated_conjecture,
( c(f(X1,X2))
| ~ d(X1)
| ~ d(X2) ),
conjecture_2 ).
cnf(c_0_10,axiom,
f(X1,f(X2,X3)) = f(f(X1,X2),X3),
f_is_associative ).
cnf(c_0_11,hypothesis,
( ~ c(f(X1,X2))
| ~ c(X2)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,negated_conjecture,
( c(f(X1,f(X2,X3)))
| ~ d(f(X1,X2))
| ~ d(X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,hypothesis,
( ~ d(f(X1,X2))
| ~ d(X3)
| ~ c(f(X2,X3))
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,axiom,
( c(X1)
| d(X1) ),
partitions_union ).
cnf(c_0_15,hypothesis,
( c(f(X1,X2))
| ~ d(X3)
| ~ c(f(X2,X3))
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,negated_conjecture,
( c(f(X1,X2))
| ~ d(X3)
| ~ d(X2)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_9]) ).
cnf(c_0_17,hypothesis,
d(a2),
partition_d_not_empty ).
cnf(c_0_18,negated_conjecture,
( ~ d(X1)
| ~ c(f(X2,X1))
| ~ c(X3)
| ~ c(X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_8]) ).
cnf(c_0_19,hypothesis,
( c(f(X1,X2))
| ~ d(X2)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
( ~ d(X1)
| ~ c(X2)
| ~ c(X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,hypothesis,
( ~ c(X1)
| ~ c(X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_22,hypothesis,
c(a1),
partition_c_not_empty ).
cnf(c_0_23,hypothesis,
~ c(X1),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,hypothesis,
$false,
inference(sr,[status(thm)],[c_0_22,c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG011-1 : TPTP v9.2.1. Released v2.7.0.
% 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
% 0.16/0.34 % Computer : n014.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue May 5 10:14:51 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------