%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM024-1 : 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 : n025.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 2.48s 2.07s
% Output : CNFRefutation 2.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 32 ( 18 unt; 0 nHn; 23 RR)
% Number of literals : 50 ( 0 equ; 27 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 58 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_a_contradiction,negated_conjecture,
~ equalish(successor(X1),n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_contradiction) ).
cnf(symmetry,axiom,
( equalish(X2,X1)
| ~ equalish(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
cnf(transitivity,axiom,
( equalish(X1,X3)
| ~ equalish(X1,X2)
| ~ equalish(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
cnf(times_zero,axiom,
equalish(multiply(X1,n0),n0),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-0.ax',times_zero) ).
cnf(commutativity_of_plus,axiom,
equalish(add(X1,X2),add(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_plus) ).
cnf(plus_substitution,axiom,
( equalish(X1,X3)
| ~ equalish(add(X1,X2),add(X3,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_substitution) ).
cnf(adding_zero,axiom,
equalish(add(X1,n0),X1),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM001-0.ax',adding_zero) ).
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(impossible_a_is_less_than_itself,hypothesis,
less(a,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',impossible_a_is_less_than_itself) ).
cnf(c_0_9,negated_conjecture,
~ equalish(successor(X1),n0),
prove_a_contradiction ).
cnf(c_0_10,axiom,
( equalish(X2,X1)
| ~ equalish(X1,X2) ),
symmetry ).
cnf(c_0_11,negated_conjecture,
~ equalish(n0,successor(X1)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,axiom,
( equalish(X1,X3)
| ~ equalish(X1,X2)
| ~ equalish(X2,X3) ),
transitivity ).
cnf(c_0_13,axiom,
equalish(multiply(X1,n0),n0),
times_zero ).
cnf(c_0_14,negated_conjecture,
( ~ equalish(X1,successor(X2))
| ~ equalish(n0,X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
equalish(n0,multiply(X1,n0)),
inference(spm,[status(thm)],[c_0_10,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
~ equalish(multiply(X1,n0),successor(X2)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,axiom,
equalish(add(X1,X2),add(X2,X1)),
commutativity_of_plus ).
cnf(c_0_18,negated_conjecture,
( ~ equalish(multiply(X1,n0),X2)
| ~ equalish(X2,successor(X3)) ),
inference(spm,[status(thm)],[c_0_16,c_0_12]) ).
cnf(c_0_19,axiom,
( equalish(X1,X3)
| ~ equalish(add(X1,X2),add(X3,X2)) ),
plus_substitution ).
cnf(c_0_20,plain,
( equalish(add(X1,X2),X3)
| ~ equalish(add(X2,X1),X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_21,axiom,
equalish(add(X1,n0),X1),
adding_zero ).
cnf(c_0_22,negated_conjecture,
( ~ equalish(multiply(X1,n0),X2)
| ~ equalish(successor(X3),X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_10]) ).
cnf(c_0_23,plain,
( equalish(X1,X2)
| ~ equalish(X3,add(X2,X4))
| ~ equalish(add(X1,X4),X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_12]) ).
cnf(c_0_24,plain,
equalish(add(n0,X1),X1),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,axiom,
( equalish(add(successor(predecessor_of_1st_minus_2nd(X2,X1)),X1),X2)
| ~ less(X1,X2) ),
less_lemma ).
cnf(c_0_26,hypothesis,
less(a,a),
impossible_a_is_less_than_itself ).
cnf(c_0_27,negated_conjecture,
( ~ equalish(add(successor(X1),X2),X3)
| ~ equalish(multiply(X4,n0),X5)
| ~ equalish(X3,add(X5,X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
equalish(X1,add(n0,X1)),
inference(spm,[status(thm)],[c_0_10,c_0_24]) ).
cnf(c_0_29,hypothesis,
equalish(add(successor(predecessor_of_1st_minus_2nd(a,a)),a),a),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
~ equalish(add(successor(X1),X2),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_13])]) ).
cnf(c_0_31,hypothesis,
$false,
inference(sr,[status(thm)],[c_0_29,c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM024-1 : 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 : n025.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 00:06:43 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 2.48/2.07 % Version : CSE_E---1.7
% 2.48/2.07 % Problem : theBenchmark.p
% 2.48/2.07 % SZS status Unsatisfiable for theBenchmark.p
% 2.48/2.07 % SZS output start CNFRefutation
% See solution above
% 2.48/2.08 % Total time : 1.368s
%------------------------------------------------------------------------------