%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM022-1 : TPTP v9.2.1. Released v1.0.0.
% 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 : n019.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 04:52:44 PM UTC 2026
% Result : Unsatisfiable 1.26s 1.71s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 23 ( 9 unt; 2 nHn; 23 RR)
% Number of literals : 45 ( 0 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity_of_less,axiom,
( less(X3,X2)
| ~ less(X1,X2)
| ~ less(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-1.ax',transitivity_of_less) ).
cnf(a_less_than_b,hypothesis,
less(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_less_than_b) ).
cnf(transitivity,axiom,
( equalish(X3,X2)
| ~ equalish(X1,X2)
| ~ equalish(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
cnf(less_lemma,axiom,
( equalish(add(successor(predecessor_of_1st_minus_2nd(X2,X1)),X1),X2)
| ~ less(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-1.ax',less_lemma) ).
cnf(prove_a_less_than_d,negated_conjecture,
~ less(a,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_less_than_d) ).
cnf(smaller_number,axiom,
( less(X2,X3)
| ~ equalish(add(successor(X1),X2),X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-1.ax',smaller_number) ).
cnf(divides_only_less_or_equal,axiom,
( less(X1,X2)
| equalish(X1,X2)
| ~ divides(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM001-2.ax',divides_only_less_or_equal) ).
cnf(b_divides_d,hypothesis,
divides(b,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_divides_d) ).
cnf(c_0_8,axiom,
( less(X3,X2)
| ~ less(X1,X2)
| ~ less(X3,X1) ),
transitivity_of_less ).
cnf(c_0_9,hypothesis,
less(a,b),
a_less_than_b ).
cnf(c_0_10,axiom,
( equalish(X3,X2)
| ~ equalish(X1,X2)
| ~ equalish(X3,X1) ),
transitivity ).
cnf(c_0_11,axiom,
( equalish(add(successor(predecessor_of_1st_minus_2nd(X2,X1)),X1),X2)
| ~ less(X1,X2) ),
less_lemma ).
cnf(c_0_12,negated_conjecture,
~ less(a,d),
prove_a_less_than_d ).
cnf(c_0_13,hypothesis,
( less(a,X1)
| ~ less(b,X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,axiom,
( less(X2,X3)
| ~ equalish(add(successor(X1),X2),X3) ),
smaller_number ).
cnf(c_0_15,plain,
( equalish(add(successor(predecessor_of_1st_minus_2nd(X1,X2)),X2),X3)
| ~ equalish(X1,X3)
| ~ less(X2,X1) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,axiom,
( less(X1,X2)
| equalish(X1,X2)
| ~ divides(X1,X2) ),
divides_only_less_or_equal ).
cnf(c_0_17,hypothesis,
divides(b,d),
b_divides_d ).
cnf(c_0_18,negated_conjecture,
~ less(b,d),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
( less(X1,X2)
| ~ equalish(X3,X2)
| ~ less(X1,X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,hypothesis,
equalish(b,d),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_21,hypothesis,
( less(X1,d)
| ~ less(X1,b) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_21]),c_0_9])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM022-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n019.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 : Tue May 5 00:06:59 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.26/1.71 % Version : CSE_E---1.7
% 1.26/1.71 % Problem : theBenchmark.p
% 1.26/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 1.26/1.71 % SZS output start CNFRefutation
% See solution above
% 1.26/1.71 % Total time : 1.370s
%------------------------------------------------------------------------------