%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GEO076-4 : 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 : n008.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 04:19:14 PM UTC 2026
% Result : Unsatisfiable 1.30s 1.73s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of clauses : 48 ( 9 unt; 21 nHn; 48 RR)
% Number of literals : 153 ( 42 equ; 85 neg)
% Maximal clause size : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_G1D,axiom,
( X1 = X3
| X2 = X4
| ~ on(X1,X2)
| ~ on(X3,X2)
| ~ on(X1,X4)
| ~ on(X3,X4)
| ~ point(X1)
| ~ point(X3)
| ~ line(X2)
| ~ line(X4) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G1D) ).
cnf(prove_point_is_not_on_every_line,negated_conjecture,
( on(a_point,X1)
| ~ line(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_point_is_not_on_every_line) ).
cnf(there_is_a_point,hypothesis,
point(a_point),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',there_is_a_point) ).
cnf(axiom_G1A,axiom,
( on(X1,line_from_to(X1,X2))
| X1 = X2
| ~ point(X1)
| ~ point(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G1A) ).
cnf(axiom_G1C,axiom,
( line(line_from_to(X1,X2))
| X1 = X2
| ~ point(X1)
| ~ point(X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G1C) ).
cnf(axiom_G2B,axiom,
( on(point_2_on_line(X1),X1)
| ~ line(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G2B) ).
cnf(axiom_G2D,axiom,
( point(point_2_on_line(X1))
| ~ line(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G2D) ).
cnf(axiom_G1B,axiom,
( on(X1,line_from_to(X2,X1))
| X2 = X1
| ~ point(X2)
| ~ point(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G1B) ).
cnf(axiom_G4A,axiom,
line(at_least_one_line),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G4A) ).
cnf(axiom_G3B,axiom,
( point(point_not_on_line(X1))
| ~ line(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G3B) ).
cnf(axiom_G3A,axiom,
( ~ on(point_not_on_line(X1),X1)
| ~ line(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G3A) ).
cnf(axiom_G2E,axiom,
( point_1_on_line(X1) != point_2_on_line(X1)
| ~ line(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G2E) ).
cnf(axiom_G2A,axiom,
( on(point_1_on_line(X1),X1)
| ~ line(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G2A) ).
cnf(axiom_G2C,axiom,
( point(point_1_on_line(X1))
| ~ line(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO003-0.ax',axiom_G2C) ).
cnf(c_0_14,axiom,
( X1 = X3
| X2 = X4
| ~ on(X1,X2)
| ~ on(X3,X2)
| ~ on(X1,X4)
| ~ on(X3,X4)
| ~ point(X1)
| ~ point(X3)
| ~ line(X2)
| ~ line(X4) ),
axiom_G1D ).
cnf(c_0_15,negated_conjecture,
( on(a_point,X1)
| ~ line(X1) ),
prove_point_is_not_on_every_line ).
cnf(c_0_16,hypothesis,
point(a_point),
there_is_a_point ).
cnf(c_0_17,negated_conjecture,
( X1 = a_point
| X2 = X3
| ~ line(X3)
| ~ line(X2)
| ~ point(X1)
| ~ on(X1,X3)
| ~ on(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]),c_0_15]) ).
cnf(c_0_18,axiom,
( on(X1,line_from_to(X1,X2))
| X1 = X2
| ~ point(X1)
| ~ point(X2) ),
axiom_G1A ).
cnf(c_0_19,axiom,
( line(line_from_to(X1,X2))
| X1 = X2
| ~ point(X1)
| ~ point(X2) ),
axiom_G1C ).
cnf(c_0_20,negated_conjecture,
( X1 = line_from_to(X2,X3)
| X2 = a_point
| X2 = X3
| ~ line(X1)
| ~ point(X2)
| ~ point(X3)
| ~ on(X2,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_21,axiom,
( on(point_2_on_line(X1),X1)
| ~ line(X1) ),
axiom_G2B ).
cnf(c_0_22,axiom,
( point(point_2_on_line(X1))
| ~ line(X1) ),
axiom_G2D ).
cnf(c_0_23,axiom,
( on(X1,line_from_to(X2,X1))
| X2 = X1
| ~ point(X2)
| ~ point(X1) ),
axiom_G1B ).
cnf(c_0_24,negated_conjecture,
( line_from_to(point_2_on_line(X1),X2) = X1
| point_2_on_line(X1) = a_point
| point_2_on_line(X1) = X2
| ~ line(X1)
| ~ point(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_25,negated_conjecture,
( point_2_on_line(X1) = a_point
| X2 = point_2_on_line(X1)
| on(X2,X1)
| ~ line(X1)
| ~ point(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_22]) ).
cnf(c_0_26,axiom,
line(at_least_one_line),
axiom_G4A ).
cnf(c_0_27,negated_conjecture,
( point_2_on_line(at_least_one_line) = a_point
| X1 = point_2_on_line(at_least_one_line)
| on(X1,at_least_one_line)
| ~ point(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_28,axiom,
( point(point_not_on_line(X1))
| ~ line(X1) ),
axiom_G3B ).
cnf(c_0_29,axiom,
( ~ on(point_not_on_line(X1),X1)
| ~ line(X1) ),
axiom_G3A ).
cnf(c_0_30,negated_conjecture,
( point_not_on_line(X1) = point_2_on_line(at_least_one_line)
| point_2_on_line(at_least_one_line) = a_point
| on(point_not_on_line(X1),at_least_one_line)
| ~ line(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
( point_not_on_line(at_least_one_line) = point_2_on_line(at_least_one_line)
| point_2_on_line(at_least_one_line) = a_point ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_26])]) ).
cnf(c_0_32,negated_conjecture,
( point_2_on_line(at_least_one_line) = a_point
| ~ on(point_2_on_line(at_least_one_line),at_least_one_line) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_31]),c_0_26])]) ).
cnf(c_0_33,plain,
( X1 = point_2_on_line(X2)
| X3 = X2
| ~ line(X2)
| ~ line(X3)
| ~ point(X1)
| ~ on(point_2_on_line(X2),X3)
| ~ on(X1,X2)
| ~ on(X1,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_21]),c_0_22]) ).
cnf(c_0_34,negated_conjecture,
point_2_on_line(at_least_one_line) = a_point,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_21]),c_0_26])]) ).
cnf(c_0_35,axiom,
( point_1_on_line(X1) != point_2_on_line(X1)
| ~ line(X1) ),
axiom_G2E ).
cnf(c_0_36,negated_conjecture,
( X1 = at_least_one_line
| X2 = a_point
| ~ line(X1)
| ~ point(X2)
| ~ on(X2,at_least_one_line)
| ~ on(X2,X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_26])]),c_0_15]) ).
cnf(c_0_37,axiom,
( on(point_1_on_line(X1),X1)
| ~ line(X1) ),
axiom_G2A ).
cnf(c_0_38,negated_conjecture,
point_1_on_line(at_least_one_line) != a_point,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_34]),c_0_26])]) ).
cnf(c_0_39,negated_conjecture,
( X1 = at_least_one_line
| ~ line(X1)
| ~ point(point_1_on_line(at_least_one_line))
| ~ on(point_1_on_line(at_least_one_line),X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_26])]),c_0_38]) ).
cnf(c_0_40,negated_conjecture,
( line_from_to(point_1_on_line(at_least_one_line),X1) = at_least_one_line
| point_1_on_line(at_least_one_line) = X1
| ~ point(point_1_on_line(at_least_one_line))
| ~ point(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_18]),c_0_19]) ).
cnf(c_0_41,negated_conjecture,
( X1 = point_1_on_line(at_least_one_line)
| on(X1,at_least_one_line)
| ~ point(point_1_on_line(at_least_one_line))
| ~ point(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_40]) ).
cnf(c_0_42,axiom,
( point(point_1_on_line(X1))
| ~ line(X1) ),
axiom_G2C ).
cnf(c_0_43,negated_conjecture,
( X1 = point_1_on_line(at_least_one_line)
| on(X1,at_least_one_line)
| ~ point(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_26])]) ).
cnf(c_0_44,negated_conjecture,
( point_not_on_line(X1) = point_1_on_line(at_least_one_line)
| on(point_not_on_line(X1),at_least_one_line)
| ~ line(X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_28]) ).
cnf(c_0_45,negated_conjecture,
point_not_on_line(at_least_one_line) = point_1_on_line(at_least_one_line),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_44]),c_0_26])]) ).
cnf(c_0_46,negated_conjecture,
~ on(point_1_on_line(at_least_one_line),at_least_one_line),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_45]),c_0_26])]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_37]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO076-4 : TPTP v9.2.1. Released v1.0.0.
% 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 : n008.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 : Mon May 4 17:39:43 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.30/1.73 % Version : CSE_E---1.7
% 1.30/1.73 % Problem : theBenchmark.p
% 1.30/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.30/1.73 % SZS output start CNFRefutation
% See solution above
% 1.30/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------