%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUN134-1 : TPTP v9.2.1. Released v8.1.0.
% 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 : n026.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 05:00:57 PM UTC 2026
% Result : Unsatisfiable 1.31s 1.72s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 33 ( 33 unt; 0 nHn; 8 RR)
% Number of literals : 33 ( 32 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(times_s,axiom,
times(s(X1),X2) = '+'(X2,times(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_s) ).
cnf(times_one,axiom,
times(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_one) ).
cnf(plus_comm,axiom,
'+'(X1,X2) = '+'(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_comm) ).
cnf(plus_assoc,axiom,
'+'(X1,'+'(X2,X3)) = '+'('+'(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_assoc) ).
cnf(plus_s,axiom,
'+'(s(X1),X2) = s('+'(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_s) ).
cnf(sum_s,axiom,
sum(s(X1)) = '+'(s(X1),sum(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_s) ).
cnf(times_comm,axiom,
times(X1,X2) = times(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',times_comm) ).
cnf(induction_hypothesis,axiom,
'+'(sum(a),sum(a)) = times(a,s(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',induction_hypothesis) ).
cnf(goal,negated_conjecture,
'+'(sum(s(a)),sum(s(a))) != times(s(a),s(s(a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
cnf(c_0_9,axiom,
times(s(X1),X2) = '+'(X2,times(X1,X2)),
times_s ).
cnf(c_0_10,axiom,
times(X1,one) = X1,
times_one ).
cnf(c_0_11,axiom,
'+'(X1,X2) = '+'(X2,X1),
plus_comm ).
cnf(c_0_12,plain,
'+'(one,X1) = s(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_10]) ).
cnf(c_0_13,plain,
'+'(X1,one) = s(X1),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,axiom,
'+'(X1,'+'(X2,X3)) = '+'('+'(X1,X2),X3),
plus_assoc ).
cnf(c_0_15,axiom,
'+'(s(X1),X2) = s('+'(X1,X2)),
plus_s ).
cnf(c_0_16,axiom,
sum(s(X1)) = '+'(s(X1),sum(X1)),
sum_s ).
cnf(c_0_17,plain,
'+'(s(X1),X2) = '+'(X1,s(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_13]),c_0_15]) ).
cnf(c_0_18,plain,
'+'(sum(X1),s(X1)) = sum(s(X1)),
inference(rw,[status(thm)],[c_0_16,c_0_11]) ).
cnf(c_0_19,plain,
'+'(X1,s(X2)) = '+'(X2,s(X1)),
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
cnf(c_0_20,axiom,
times(X1,X2) = times(X2,X1),
times_comm ).
cnf(c_0_21,axiom,
'+'(sum(a),sum(a)) = times(a,s(a)),
induction_hypothesis ).
cnf(c_0_22,plain,
s('+'(X1,X2)) = '+'(X1,s(X2)),
inference(rw,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_23,plain,
'+'(X1,s(sum(X1))) = sum(s(X1)),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
times(one,X1) = X1,
inference(spm,[status(thm)],[c_0_10,c_0_20]) ).
cnf(c_0_25,plain,
'+'(a,'+'(sum(a),s(sum(a)))) = times(s(a),s(a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_21]),c_0_17]),c_0_22]) ).
cnf(c_0_26,plain,
'+'(X1,'+'(sum(X1),s(X2))) = '+'(sum(s(X1)),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_23]),c_0_17]) ).
cnf(c_0_27,negated_conjecture,
'+'(sum(s(a)),sum(s(a))) != times(s(a),s(s(a))),
goal ).
cnf(c_0_28,plain,
'+'(X1,X1) = times(s(one),X1),
inference(spm,[status(thm)],[c_0_9,c_0_24]) ).
cnf(c_0_29,plain,
'+'(X1,times(X1,X2)) = times(s(X2),X1),
inference(spm,[status(thm)],[c_0_9,c_0_20]) ).
cnf(c_0_30,plain,
times(s(a),s(a)) = '+'(sum(a),sum(s(a))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_11]) ).
cnf(c_0_31,negated_conjecture,
times(s(a),s(s(a))) != times(s(one),sum(s(a))),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_17]),c_0_22]),c_0_26]),c_0_28]),c_0_20]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : NUN134-1 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.10 % 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
% 0.13/0.31 % Computer : n026.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Tue May 5 01:24:38 EDT 2026
% 0.13/0.31 % CPUTime :
% 0.13/0.33 % start to proof: theBenchmark
% 1.31/1.72 % Version : CSE_E---1.7
% 1.31/1.72 % Problem : theBenchmark.p
% 1.31/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.31/1.72 % SZS output start CNFRefutation
% See solution above
% 1.31/1.72 % Total time : 1.370s
%------------------------------------------------------------------------------