%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ANA003-2 : 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 04:09:15 PM UTC 2026
% Result : Unsatisfiable 7.33s 5.39s
% Output : CNFRefutation 7.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of clauses : 37 ( 4 unt; 0 nHn; 37 RR)
% Number of literals : 98 ( 0 equ; 67 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(transitivity_of_less_than,axiom,
( less_than(X1,X3)
| ~ less_than(X1,X2)
| ~ less_than(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_less_than) ).
cnf(axiom_2_3,axiom,
( less_than(minimum(X1,X2),X2)
| ~ less_than(n0,X1)
| ~ less_than(n0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2_3) ).
cnf(axiom_3,axiom,
( less_than(add(X1,X3),X2)
| ~ less_than(X1,half(X2))
| ~ less_than(X3,half(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
cnf(c_13,negated_conjecture,
( less_than(absolute(add(g(X2),minus(l2))),X1)
| ~ less_than(n0,X1)
| ~ less_than(absolute(add(X2,minus(a))),fp32(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_13) ).
cnf(c_15,negated_conjecture,
( less_than(absolute(add(fp33(X1),minus(a))),X1)
| ~ less_than(n0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_15) ).
cnf(axiom_2_1,axiom,
( less_than(n0,minimum(X1,X2))
| ~ less_than(n0,X1)
| ~ less_than(n0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2_1) ).
cnf(c_12,negated_conjecture,
( less_than(n0,fp32(X1))
| ~ less_than(n0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_12) ).
cnf(c_16,negated_conjecture,
( ~ less_than(n0,X1)
| ~ less_than(add(absolute(add(f(fp33(X1)),minus(l1))),absolute(add(g(fp33(X1)),minus(l2)))),b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_16) ).
cnf(axiom_2_2,axiom,
( less_than(minimum(X1,X2),X1)
| ~ less_than(n0,X1)
| ~ less_than(n0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2_2) ).
cnf(c_11,negated_conjecture,
( less_than(absolute(add(f(X2),minus(l1))),X1)
| ~ less_than(n0,X1)
| ~ less_than(absolute(add(X2,minus(a))),fp31(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_11) ).
cnf(c_10,negated_conjecture,
( less_than(n0,fp31(X1))
| ~ less_than(n0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_10) ).
cnf(axiom_7,axiom,
( less_than(n0,half(X1))
| ~ less_than(n0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
cnf(c_14,negated_conjecture,
less_than(n0,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_14) ).
cnf(c_0_13,axiom,
( less_than(X1,X3)
| ~ less_than(X1,X2)
| ~ less_than(X2,X3) ),
transitivity_of_less_than ).
cnf(c_0_14,axiom,
( less_than(minimum(X1,X2),X2)
| ~ less_than(n0,X1)
| ~ less_than(n0,X2) ),
axiom_2_3 ).
cnf(c_0_15,axiom,
( less_than(add(X1,X3),X2)
| ~ less_than(X1,half(X2))
| ~ less_than(X3,half(X2)) ),
axiom_3 ).
cnf(c_0_16,negated_conjecture,
( less_than(absolute(add(g(X2),minus(l2))),X1)
| ~ less_than(n0,X1)
| ~ less_than(absolute(add(X2,minus(a))),fp32(X1)) ),
c_13 ).
cnf(c_0_17,plain,
( less_than(X1,X2)
| ~ less_than(X1,minimum(X3,X2))
| ~ less_than(n0,X2)
| ~ less_than(n0,X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( less_than(absolute(add(fp33(X1),minus(a))),X1)
| ~ less_than(n0,X1) ),
c_15 ).
cnf(c_0_19,axiom,
( less_than(n0,minimum(X1,X2))
| ~ less_than(n0,X1)
| ~ less_than(n0,X2) ),
axiom_2_1 ).
cnf(c_0_20,negated_conjecture,
( less_than(add(X1,absolute(add(g(X2),minus(l2)))),X3)
| ~ less_than(absolute(add(X2,minus(a))),fp32(half(X3)))
| ~ less_than(n0,half(X3))
| ~ less_than(X1,half(X3)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( less_than(absolute(add(fp33(minimum(X1,X2)),minus(a))),X2)
| ~ less_than(n0,X2)
| ~ less_than(n0,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_22,negated_conjecture,
( less_than(n0,fp32(X1))
| ~ less_than(n0,X1) ),
c_12 ).
cnf(c_0_23,negated_conjecture,
( ~ less_than(n0,X1)
| ~ less_than(add(absolute(add(f(fp33(X1)),minus(l1))),absolute(add(g(fp33(X1)),minus(l2)))),b) ),
c_16 ).
cnf(c_0_24,negated_conjecture,
( less_than(add(X1,absolute(add(g(fp33(minimum(X2,fp32(half(X3))))),minus(l2)))),X3)
| ~ less_than(n0,half(X3))
| ~ less_than(X1,half(X3))
| ~ less_than(n0,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_25,axiom,
( less_than(minimum(X1,X2),X1)
| ~ less_than(n0,X1)
| ~ less_than(n0,X2) ),
axiom_2_2 ).
cnf(c_0_26,negated_conjecture,
( ~ less_than(absolute(add(f(fp33(minimum(X1,fp32(half(b))))),minus(l1))),half(b))
| ~ less_than(n0,minimum(X1,fp32(half(b))))
| ~ less_than(n0,half(b))
| ~ less_than(n0,X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,negated_conjecture,
( less_than(absolute(add(f(X2),minus(l1))),X1)
| ~ less_than(n0,X1)
| ~ less_than(absolute(add(X2,minus(a))),fp31(X1)) ),
c_11 ).
cnf(c_0_28,plain,
( less_than(X1,X2)
| ~ less_than(X1,minimum(X2,X3))
| ~ less_than(n0,X3)
| ~ less_than(n0,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( ~ less_than(absolute(add(fp33(minimum(X1,fp32(half(b)))),minus(a))),fp31(half(b)))
| ~ less_than(n0,minimum(X1,fp32(half(b))))
| ~ less_than(n0,half(b))
| ~ less_than(n0,X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( less_than(absolute(add(fp33(minimum(X1,X2)),minus(a))),X1)
| ~ less_than(n0,X2)
| ~ less_than(n0,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_18]),c_0_19]) ).
cnf(c_0_31,negated_conjecture,
( less_than(n0,fp31(X1))
| ~ less_than(n0,X1) ),
c_10 ).
cnf(c_0_32,negated_conjecture,
( ~ less_than(n0,minimum(fp31(half(b)),fp32(half(b))))
| ~ less_than(n0,half(b)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_22]),c_0_31]) ).
cnf(c_0_33,negated_conjecture,
~ less_than(n0,half(b)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_19]),c_0_31]),c_0_22]) ).
cnf(c_0_34,axiom,
( less_than(n0,half(X1))
| ~ less_than(n0,X1) ),
axiom_7 ).
cnf(c_0_35,negated_conjecture,
less_than(n0,b),
c_14 ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ANA003-2 : 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 10:34:51 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 7.33/5.39 % Version : CSE_E---1.7
% 7.33/5.39 % Problem : theBenchmark.p
% 7.33/5.39 % SZS status Unsatisfiable for theBenchmark.p
% 7.33/5.39 % SZS output start CNFRefutation
% See solution above
% 7.43/5.40 % Total time : 4.371s
%------------------------------------------------------------------------------