%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ROB016-1 : TPTP v9.2.1. Released v1.0.0.
% 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 : 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 05:05:44 PM UTC 2026
% Result : Unsatisfiable 1.33s 1.74s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of clauses : 17 ( 14 unt; 0 nHn; 12 RR)
% Number of literals : 22 ( 16 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 3 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(robbins_axiom,axiom,
negate(add(negate(add(X1,X2)),negate(add(X1,negate(X2))))) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/ROB001-0.ax',robbins_axiom) ).
cnf(commutativity_of_add,axiom,
add(X1,X2) = add(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/ROB001-0.ax',commutativity_of_add) ).
cnf(condition,hypothesis,
negate(add(d,e)) = negate(e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condition) ).
cnf(lemma_3_6,axiom,
( negate(add(X1,multiply(X3,add(X2,negate(add(X2,negate(X1))))))) = negate(X1)
| negate(add(negate(X1),negate(add(X2,negate(X1))))) != X2
| ~ positive_integer(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_3_6) ).
cnf(k_positive,axiom,
positive_integer(k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_positive) ).
cnf(prove_result,negated_conjecture,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) != negate(e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_result) ).
cnf(c_0_6,axiom,
negate(add(negate(add(X1,X2)),negate(add(X1,negate(X2))))) = X1,
robbins_axiom ).
cnf(c_0_7,axiom,
add(X1,X2) = add(X2,X1),
commutativity_of_add ).
cnf(c_0_8,hypothesis,
negate(add(d,e)) = negate(e),
condition ).
cnf(c_0_9,plain,
negate(add(negate(add(X1,X2)),negate(add(X2,negate(X1))))) = X2,
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,hypothesis,
negate(add(e,d)) = negate(e),
inference(rw,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_11,axiom,
( negate(add(X1,multiply(X3,add(X2,negate(add(X2,negate(X1))))))) = negate(X1)
| negate(add(negate(X1),negate(add(X2,negate(X1))))) != X2
| ~ positive_integer(X3) ),
lemma_3_6 ).
cnf(c_0_12,hypothesis,
negate(add(negate(e),negate(add(d,negate(e))))) = d,
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,hypothesis,
( negate(add(e,multiply(X1,add(d,negate(add(d,negate(e))))))) = negate(e)
| ~ positive_integer(X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,axiom,
positive_integer(k),
k_positive ).
cnf(c_0_15,negated_conjecture,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) != negate(e),
prove_result ).
cnf(c_0_16,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ROB016-1 : TPTP v9.2.1. Released v1.0.0.
% 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
% 0.14/0.32 % Computer : n016.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 01:53:51 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.33/1.74 % Version : CSE_E---1.7
% 1.33/1.74 % Problem : theBenchmark.p
% 1.33/1.74 % SZS status Unsatisfiable for theBenchmark.p
% 1.33/1.74 % SZS output start CNFRefutation
% See solution above
% 1.33/1.74 % Total time : 1.371s
%------------------------------------------------------------------------------