%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : RNG055+2 : TPTP v9.2.1. Released 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 : 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 05:05:08 PM UTC 2026
% Result : Theorem 1.93s 1.92s
% Output : CNFRefutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 10 unt; 0 def)
% Number of atoms : 77 ( 24 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 91 ( 42 ~; 34 |; 13 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 21 ( 1 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mArith,axiom,
! [X1,X2,X3] :
( ( aScalar0(X1)
& aScalar0(X2)
& aScalar0(X3) )
=> ( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
& sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
& sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
& sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArith) ).
fof(m__,conjecture,
sdtasdt0(xP,xP) = sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__1949,hypothesis,
( aScalar0(xN)
& xN = sdtasdt0(xR,xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1949) ).
fof(m__1820,hypothesis,
( aScalar0(xE)
& xE = sdtasasdt0(xp,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1820) ).
fof(m__1911,hypothesis,
( aScalar0(xP)
& xP = sdtasdt0(xE,xH) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1911) ).
fof(m__1873,hypothesis,
( aScalar0(xH)
& xH = sdtasdt0(xA,xB) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1873) ).
fof(mMulSc,axiom,
! [X1,X2] :
( ( aScalar0(X1)
& aScalar0(X2) )
=> aScalar0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulSc) ).
fof(c_0_7,plain,
! [X90,X91,X92] :
( ( sdtpldt0(sdtpldt0(X90,X91),X92) = sdtpldt0(X90,sdtpldt0(X91,X92))
| ~ aScalar0(X90)
| ~ aScalar0(X91)
| ~ aScalar0(X92) )
& ( sdtpldt0(X90,X91) = sdtpldt0(X91,X90)
| ~ aScalar0(X90)
| ~ aScalar0(X91)
| ~ aScalar0(X92) )
& ( sdtasdt0(sdtasdt0(X90,X91),X92) = sdtasdt0(X90,sdtasdt0(X91,X92))
| ~ aScalar0(X90)
| ~ aScalar0(X91)
| ~ aScalar0(X92) )
& ( sdtasdt0(X90,X91) = sdtasdt0(X91,X90)
| ~ aScalar0(X90)
| ~ aScalar0(X91)
| ~ aScalar0(X92) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mArith])])]) ).
fof(c_0_8,negated_conjecture,
sdtasdt0(xP,xP) != sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_9,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,hypothesis,
aScalar0(xN),
inference(split_conjunct,[status(thm)],[m__1949]) ).
cnf(c_0_11,negated_conjecture,
sdtasdt0(xP,xP) != sdtasdt0(sdtasdt0(xH,xH),sdtasdt0(xE,xE)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,hypothesis,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aScalar0(X2)
| ~ aScalar0(X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
( sdtasdt0(sdtasdt0(xE,xE),sdtasdt0(xH,xH)) != sdtasdt0(xP,xP)
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xE,xE)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aScalar0(X1)
| ~ aScalar0(X2)
| ~ aScalar0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,hypothesis,
aScalar0(xE),
inference(split_conjunct,[status(thm)],[m__1820]) ).
cnf(c_0_16,hypothesis,
xP = sdtasdt0(xE,xH),
inference(split_conjunct,[status(thm)],[m__1911]) ).
cnf(c_0_17,hypothesis,
aScalar0(xH),
inference(split_conjunct,[status(thm)],[m__1873]) ).
cnf(c_0_18,negated_conjecture,
( sdtasdt0(xE,sdtasdt0(xE,sdtasdt0(xH,xH))) != sdtasdt0(xP,xP)
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xE,xE)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_19,hypothesis,
( sdtasdt0(xE,sdtasdt0(xH,X1)) = sdtasdt0(xP,X1)
| ~ aScalar0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_16]),c_0_17]),c_0_15])]) ).
cnf(c_0_20,hypothesis,
( sdtasdt0(xE,sdtasdt0(xP,xH)) != sdtasdt0(xP,xP)
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xE,xE)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_17])]) ).
cnf(c_0_21,hypothesis,
aScalar0(xP),
inference(split_conjunct,[status(thm)],[m__1911]) ).
cnf(c_0_22,hypothesis,
( sdtasdt0(xE,sdtasdt0(xH,xP)) != sdtasdt0(xP,xP)
| ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xE,xE)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_12]),c_0_17]),c_0_21])]) ).
fof(c_0_23,plain,
! [X86,X87] :
( ~ aScalar0(X86)
| ~ aScalar0(X87)
| aScalar0(sdtasdt0(X86,X87)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulSc])]) ).
cnf(c_0_24,hypothesis,
( ~ aScalar0(sdtasdt0(xH,xH))
| ~ aScalar0(sdtasdt0(xE,xE)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_19]),c_0_21])]) ).
cnf(c_0_25,plain,
( aScalar0(sdtasdt0(X1,X2))
| ~ aScalar0(X1)
| ~ aScalar0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_26,hypothesis,
~ aScalar0(sdtasdt0(xE,xE)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_17])]) ).
cnf(c_0_27,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_25]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG055+2 : TPTP v9.2.1. Released 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 : n016.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 01:49:51 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.93/1.92 % Version : CSE_E---1.7
% 1.93/1.92 % Problem : theBenchmark.p
% 1.93/1.92 % SZS status Theorem for theBenchmark.p
% 1.93/1.92 % SZS output start CNFRefutation
% See solution above
% 1.93/1.92 % Total time : 1.368s
%------------------------------------------------------------------------------