%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM027-1 : TPTP v9.2.1. Bugfixed 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 : n015.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 04:52:45 PM UTC 2026
% Result : Unsatisfiable 1.62s 1.82s
% Output : CNFRefutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of clauses : 35 ( 15 unt; 5 nHn; 23 RR)
% Number of literals : 63 ( 0 equ; 29 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 55 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity_of_less,axiom,
( less(X3,X2)
| ~ less(X1,X2)
| ~ less(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-1.ax',transitivity_of_less) ).
cnf(b_times_c_less_than_a_times_c,hypothesis,
less(multiply(b,c),multiply(a,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_times_c_less_than_a_times_c) ).
cnf(smaller_number,axiom,
( less(X2,X3)
| ~ equalish(add(successor(X1),X2),X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-1.ax',smaller_number) ).
cnf(reflexivity,axiom,
equalish(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
cnf(not_less_and_equal,axiom,
( ~ less(X1,X2)
| ~ equalish(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_less_and_equal) ).
cnf(symmetry,axiom,
( equalish(X2,X1)
| ~ equalish(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
cnf(less_lemma,axiom,
( equalish(add(successor(predecessor_of_1st_minus_2nd(X2,X1)),X1),X2)
| ~ less(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-1.ax',less_lemma) ).
cnf(equality_preserved_over_times,axiom,
( equalish(multiply(X1,X3),multiply(X2,X3))
| ~ equalish(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality_preserved_over_times) ).
cnf(multiply_lemma,axiom,
( equalish(X3,n0)
| less(multiply(X1,X3),multiply(X2,X3))
| ~ less(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_lemma) ).
cnf(numbers_either_less_or_equal,axiom,
( less(X1,X2)
| equalish(X2,X1)
| less(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',numbers_either_less_or_equal) ).
cnf(b_not_less_than_a,hypothesis,
~ less(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_not_less_than_a) ).
cnf(prove_c_is_0,negated_conjecture,
~ equalish(c,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_is_0) ).
cnf(c_0_12,axiom,
( less(X3,X2)
| ~ less(X1,X2)
| ~ less(X3,X1) ),
transitivity_of_less ).
cnf(c_0_13,hypothesis,
less(multiply(b,c),multiply(a,c)),
b_times_c_less_than_a_times_c ).
cnf(c_0_14,axiom,
( less(X2,X3)
| ~ equalish(add(successor(X1),X2),X3) ),
smaller_number ).
cnf(c_0_15,axiom,
equalish(X1,X1),
reflexivity ).
cnf(c_0_16,hypothesis,
( less(multiply(b,c),X1)
| ~ less(multiply(a,c),X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
less(X1,add(successor(X2),X1)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,axiom,
( ~ less(X1,X2)
| ~ equalish(X1,X2) ),
not_less_and_equal ).
cnf(c_0_19,hypothesis,
less(multiply(b,c),add(successor(X1),multiply(a,c))),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,axiom,
( equalish(X2,X1)
| ~ equalish(X1,X2) ),
symmetry ).
cnf(c_0_21,axiom,
( equalish(add(successor(predecessor_of_1st_minus_2nd(X2,X1)),X1),X2)
| ~ less(X1,X2) ),
less_lemma ).
cnf(c_0_22,axiom,
( equalish(multiply(X1,X3),multiply(X2,X3))
| ~ equalish(X1,X2) ),
equality_preserved_over_times ).
cnf(c_0_23,hypothesis,
~ equalish(multiply(b,c),add(successor(X1),multiply(a,c))),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( equalish(X1,add(successor(predecessor_of_1st_minus_2nd(X1,X2)),X2))
| ~ less(X2,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,axiom,
( equalish(X3,n0)
| less(multiply(X1,X3),multiply(X2,X3))
| ~ less(X1,X2) ),
multiply_lemma ).
cnf(c_0_26,axiom,
( less(X1,X2)
| equalish(X2,X1)
| less(X2,X1) ),
numbers_either_less_or_equal ).
cnf(c_0_27,hypothesis,
~ equalish(multiply(b,c),multiply(a,c)),
inference(spm,[status(thm)],[c_0_18,c_0_13]) ).
cnf(c_0_28,plain,
( equalish(multiply(X1,X2),multiply(X3,X2))
| ~ equalish(X3,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_22]) ).
cnf(c_0_29,hypothesis,
~ less(multiply(a,c),multiply(b,c)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,plain,
( less(multiply(X1,X2),multiply(X3,X2))
| less(X3,X1)
| equalish(X2,n0)
| equalish(X1,X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,hypothesis,
~ less(b,a),
b_not_less_than_a ).
cnf(c_0_32,negated_conjecture,
~ equalish(c,n0),
prove_c_is_0 ).
cnf(c_0_33,hypothesis,
~ equalish(a,b),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,hypothesis,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM027-1 : TPTP v9.2.1. Bugfixed 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
% 0.16/0.33 % Computer : n015.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 : Tue May 5 00:07:16 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.62/1.82 % Version : CSE_E---1.7
% 1.62/1.82 % Problem : theBenchmark.p
% 1.62/1.82 % SZS status Unsatisfiable for theBenchmark.p
% 1.62/1.82 % SZS output start CNFRefutation
% See solution above
% 1.62/1.82 % Total time : 1.373s
%------------------------------------------------------------------------------