%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYO691-1.001 : TPTP v9.2.1. Released v7.3.0.
% 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 : n016.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 05:54:40 PM UTC 2026
% Result : Unsatisfiable 17.50s 12.18s
% Output : CNFRefutation 17.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 7
% Syntax : Number of clauses : 33 ( 9 unt; 0 nHn; 23 RR)
% Number of literals : 68 ( 0 equ; 41 neg)
% Maximal clause size : 3 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 111 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(rewrite_sequence_succ,axiom,
( seq(succ(X1),X2,X4)
| ~ seq(X1,X2,X3)
| ~ step(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_sequence_succ) ).
cnf(rewrite_sequence_zero,axiom,
seq(zero,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_sequence_zero) ).
cnf(rewrite_left,axiom,
( step(f(X1,X3),f(X2,X3))
| ~ step(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_left) ).
cnf(rewrite_top,axiom,
( step(X1,X2)
| ~ top(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_top) ).
cnf(rule_1,axiom,
top(f(f(f(X1,a),X2),f(X3,a)),f(f(X3,f(f(X2,a),a)),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).
cnf(rewrite_right,axiom,
( step(f(X3,X1),f(X3,X2))
| ~ step(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rewrite_right) ).
cnf(prove,negated_conjecture,
~ seq(succ(succ(succ(succ(succ(zero))))),X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
cnf(c_0_7,axiom,
( seq(succ(X1),X2,X4)
| ~ seq(X1,X2,X3)
| ~ step(X3,X4) ),
rewrite_sequence_succ ).
cnf(c_0_8,axiom,
seq(zero,X1,X1),
rewrite_sequence_zero ).
cnf(c_0_9,plain,
( seq(succ(zero),X1,X2)
| ~ step(X1,X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,plain,
( seq(succ(succ(zero)),X1,X2)
| ~ step(X3,X2)
| ~ step(X1,X3) ),
inference(spm,[status(thm)],[c_0_7,c_0_9]) ).
cnf(c_0_11,axiom,
( step(f(X1,X3),f(X2,X3))
| ~ step(X1,X2) ),
rewrite_left ).
cnf(c_0_12,axiom,
( step(X1,X2)
| ~ top(X1,X2) ),
rewrite_top ).
cnf(c_0_13,axiom,
top(f(f(f(X1,a),X2),f(X3,a)),f(f(X3,f(f(X2,a),a)),X1)),
rule_1 ).
cnf(c_0_14,plain,
( seq(succ(succ(zero)),X1,f(X2,X3))
| ~ step(X1,f(X4,X3))
| ~ step(X4,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
step(f(f(f(X1,a),X2),f(X3,a)),f(f(X3,f(f(X2,a),a)),X1)),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,plain,
( seq(succ(succ(zero)),f(f(f(X1,a),X2),f(X3,a)),f(X4,X1))
| ~ step(f(X3,f(f(X2,a),a)),X4) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,plain,
( seq(succ(succ(succ(zero))),f(f(f(X1,a),X2),f(X3,a)),X4)
| ~ step(f(X3,f(f(X2,a),a)),X5)
| ~ step(f(X5,X1),X4) ),
inference(spm,[status(thm)],[c_0_7,c_0_16]) ).
cnf(c_0_18,plain,
( seq(succ(succ(succ(zero))),f(f(f(X1,a),X2),f(f(f(X3,a),X4),a)),X5)
| ~ step(f(f(f(f(X2,a),f(f(X4,a),a)),X3),X1),X5) ),
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_19,plain,
( seq(succ(succ(succ(succ(zero)))),f(f(f(X1,a),X2),f(f(f(X3,a),X4),a)),X5)
| ~ step(f(f(f(f(X2,a),f(f(X4,a),a)),X3),X1),X6)
| ~ step(X6,X5) ),
inference(spm,[status(thm)],[c_0_7,c_0_18]) ).
cnf(c_0_20,plain,
( seq(succ(succ(succ(succ(zero)))),f(f(f(X1,a),X2),f(f(f(X3,a),X4),a)),X5)
| ~ step(f(f(f(X2,a),f(f(X4,a),a)),X3),X6)
| ~ step(f(X6,X1),X5) ),
inference(spm,[status(thm)],[c_0_19,c_0_11]) ).
cnf(c_0_21,plain,
( seq(succ(succ(succ(succ(zero)))),f(f(f(X1,a),X2),f(f(f(X3,a),X4),a)),X5)
| ~ step(f(f(X2,a),f(f(X4,a),a)),X6)
| ~ step(f(f(X6,X3),X1),X5) ),
inference(spm,[status(thm)],[c_0_20,c_0_11]) ).
cnf(c_0_22,plain,
( seq(succ(succ(succ(succ(zero)))),f(f(f(X1,a),f(X2,a)),f(f(f(X3,a),X4),a)),X5)
| ~ step(f(f(f(f(f(X4,a),f(f(a,a),a)),X2),X3),X1),X5) ),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_23,plain,
( seq(succ(succ(succ(succ(succ(zero))))),f(f(f(X1,a),f(X2,a)),f(f(f(X3,a),X4),a)),X5)
| ~ step(f(f(f(f(f(X4,a),f(f(a,a),a)),X2),X3),X1),X6)
| ~ step(X6,X5) ),
inference(spm,[status(thm)],[c_0_7,c_0_22]) ).
cnf(c_0_24,axiom,
( step(f(X3,X1),f(X3,X2))
| ~ step(X1,X2) ),
rewrite_right ).
cnf(c_0_25,plain,
( seq(succ(succ(succ(succ(succ(zero))))),f(f(f(X1,a),f(X2,a)),f(f(f(X3,a),X4),a)),X5)
| ~ step(f(f(f(f(f(X4,a),f(f(a,a),a)),X2),X3),X6),X5)
| ~ step(X1,X6) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,negated_conjecture,
~ seq(succ(succ(succ(succ(succ(zero))))),X1,X1),
prove ).
cnf(c_0_27,plain,
( seq(succ(succ(succ(succ(succ(zero))))),f(f(f(X1,a),f(X2,a)),f(f(f(X3,a),X4),a)),f(X5,X6))
| ~ step(f(f(f(f(X4,a),f(f(a,a),a)),X2),X3),X5)
| ~ step(X1,X6) ),
inference(spm,[status(thm)],[c_0_25,c_0_11]) ).
cnf(c_0_28,negated_conjecture,
( ~ step(f(f(f(f(X1,a),f(f(a,a),a)),X2),X3),f(f(X4,a),f(X2,a)))
| ~ step(X4,f(f(f(X3,a),X1),a)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,negated_conjecture,
( ~ step(f(f(f(X1,a),f(f(a,a),a)),X2),f(X3,a))
| ~ step(X3,f(f(f(f(X2,a),a),X1),a)) ),
inference(spm,[status(thm)],[c_0_28,c_0_11]) ).
cnf(c_0_30,negated_conjecture,
( ~ step(X1,f(f(f(f(a,a),a),X2),a))
| ~ step(f(f(X2,a),f(f(a,a),a)),X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_11]) ).
cnf(c_0_31,negated_conjecture,
~ step(f(f(f(f(X1,a),a),a),f(f(a,a),a)),f(f(f(a,a),X1),f(f(f(a,a),a),a))),
inference(spm,[status(thm)],[c_0_30,c_0_15]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_31,c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO691-1.001 : TPTP v9.2.1. Released v7.3.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n016.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 09:21:36 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 17.50/12.18 % Version : CSE_E---1.7
% 17.50/12.18 % Problem : theBenchmark.p
% 17.50/12.18 % SZS status Unsatisfiable for theBenchmark.p
% 17.50/12.18 % SZS output start CNFRefutation
% See solution above
% 17.50/12.19 % Total time : 11.393s
%------------------------------------------------------------------------------