%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : GEO456+1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:30:13 PM UTC 2026
% Result : Theorem 14.89s 3.66s
% Output : CNFRefutation 14.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 31 unt; 0 def)
% Number of atoms : 31 ( 30 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 17 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 21 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(aLIFTu_EQu_CMUL,conjecture,
! [X1] : s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X1))) = s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),i(s(fun(real,fun(cart(real,n10),cart(real,n10))),r_),s(real,X1))),s(cart(real,n10),i(s(fun(num,cart(real,n10)),vec),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aLIFTu_EQu_CMUL) ).
fof(aLIFTu_NUM,axiom,
! [X84] : s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(num,real),realu_ofu_num),s(num,X84))))) = s(cart(real,n10),i(s(fun(num,cart(real,n10)),vec),s(num,X84))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aLIFTu_NUM) ).
fof(aintu_ofu_numu_th,axiom,
! [X84] : s(real,i(s(fun(int,real),realu_ofu_int),s(int,i(s(fun(num,int),intu_ofu_num),s(num,X84))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,X84))),
file('/export/starexec/sandbox/benchmark/Axioms/GEO010+0.ax',aintu_ofu_numu_th) ).
fof(aBIT1u_DEF,axiom,
! [X84] : s(num,i(s(fun(num,num),bit1),s(num,X84))) = s(num,i(s(fun(num,num),suc),s(num,i(s(fun(num,num),bit0),s(num,X84))))),
file('/export/starexec/sandbox/benchmark/Axioms/GEO010+0.ax',aBIT1u_DEF) ).
fof(aSUCu_DEF,axiom,
! [X84] : s(num,i(s(fun(num,num),suc),s(num,X84))) = s(num,i(s(fun(ind0,num),mku_num),s(ind0,i(s(fun(ind0,ind0),indu_suc),s(ind0,i(s(fun(num,ind0),destu_num),s(num,X84))))))),
file('/export/starexec/sandbox/benchmark/Axioms/GEO010+0.ax',aSUCu_DEF) ).
fof(aNUMERAL,axiom,
! [X84] : s(num,i(s(fun(num,num),numeral),s(num,X84))) = s(num,X84),
file('/export/starexec/sandbox/benchmark/Axioms/GEO010+0.ax',aNUMERAL) ).
fof(aREALu_MULu_RID,axiom,
! [X1] : s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X1))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(real,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GEO010+0.ax',aREALu_MULu_RID) ).
fof(aARITHu_ZEROu_conjunct1,axiom,
s(num,i(s(fun(num,num),bit0),s(num,u_0))) = s(num,u_0),
file('/export/starexec/sandbox/benchmark/Axioms/GEO010+0.ax',aARITHu_ZEROu_conjunct1) ).
fof(aLIFTu_CMUL,axiom,
! [X1,X95] : s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X95))),s(real,X1))))) = s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),i(s(fun(real,fun(cart(real,n10),cart(real,n10))),r_),s(real,X95))),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X1))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aLIFTu_CMUL) ).
fof(c_0_9,negated_conjecture,
~ ! [X1] : s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X1))) = s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),i(s(fun(real,fun(cart(real,n10),cart(real,n10))),r_),s(real,X1))),s(cart(real,n10),i(s(fun(num,cart(real,n10)),vec),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),
inference(assume_negation,[status(cth)],[aLIFTu_EQu_CMUL]) ).
fof(c_0_10,plain,
! [X16628] : s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(num,real),realu_ofu_num),s(num,X16628))))) = s(cart(real,n10),i(s(fun(num,cart(real,n10)),vec),s(num,X16628))),
inference(variable_rename,[status(thm)],[aLIFTu_NUM]) ).
fof(c_0_11,plain,
! [X5528] : s(real,i(s(fun(int,real),realu_ofu_int),s(int,i(s(fun(num,int),intu_ofu_num),s(num,X5528))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,X5528))),
inference(variable_rename,[status(thm)],[aintu_ofu_numu_th]) ).
fof(c_0_12,negated_conjecture,
s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,esk3826_0))) != s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),i(s(fun(real,fun(cart(real,n10),cart(real,n10))),r_),s(real,esk3826_0))),s(cart(real,n10),i(s(fun(num,cart(real,n10)),vec),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_13,plain,
! [X2401] : s(num,i(s(fun(num,num),bit1),s(num,X2401))) = s(num,i(s(fun(num,num),suc),s(num,i(s(fun(num,num),bit0),s(num,X2401))))),
inference(variable_rename,[status(thm)],[aBIT1u_DEF]) ).
fof(c_0_14,plain,
! [X2368] : s(num,i(s(fun(num,num),suc),s(num,X2368))) = s(num,i(s(fun(ind0,num),mku_num),s(ind0,i(s(fun(ind0,ind0),indu_suc),s(ind0,i(s(fun(num,ind0),destu_num),s(num,X2368))))))),
inference(variable_rename,[status(thm)],[aSUCu_DEF]) ).
fof(c_0_15,plain,
! [X2371] : s(num,i(s(fun(num,num),numeral),s(num,X2371))) = s(num,X2371),
inference(variable_rename,[status(thm)],[aNUMERAL]) ).
cnf(c_0_16,plain,
s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(num,real),realu_ofu_num),s(num,X1))))) = s(cart(real,n10),i(s(fun(num,cart(real,n10)),vec),s(num,X1))),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
s(real,i(s(fun(int,real),realu_ofu_int),s(int,i(s(fun(num,int),intu_ofu_num),s(num,X1))))) = s(real,i(s(fun(num,real),realu_ofu_num),s(num,X1))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_18,plain,
! [X4932] : s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X4932))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(real,X4932),
inference(variable_rename,[status(thm)],[aREALu_MULu_RID]) ).
cnf(c_0_19,negated_conjecture,
s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,esk3826_0))) != s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),i(s(fun(real,fun(cart(real,n10),cart(real,n10))),r_),s(real,esk3826_0))),s(cart(real,n10),i(s(fun(num,cart(real,n10)),vec),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
s(num,i(s(fun(num,num),bit1),s(num,X1))) = s(num,i(s(fun(num,num),suc),s(num,i(s(fun(num,num),bit0),s(num,X1))))),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
s(num,i(s(fun(num,num),bit0),s(num,u_0))) = s(num,u_0),
inference(split_conjunct,[status(thm)],[aARITHu_ZEROu_conjunct1]) ).
cnf(c_0_22,plain,
s(num,i(s(fun(num,num),suc),s(num,X1))) = s(num,i(s(fun(ind0,num),mku_num),s(ind0,i(s(fun(ind0,ind0),indu_suc),s(ind0,i(s(fun(num,ind0),destu_num),s(num,X1))))))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
s(num,i(s(fun(num,num),numeral),s(num,X1))) = s(num,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
s(cart(real,n10),i(s(fun(num,cart(real,n10)),vec),s(num,X1))) = s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(int,real),realu_ofu_int),s(int,i(s(fun(num,int),intu_ofu_num),s(num,X1))))))),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_25,plain,
! [X16633,X16634] : s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X16634))),s(real,X16633))))) = s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),i(s(fun(real,fun(cart(real,n10),cart(real,n10))),r_),s(real,X16634))),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X16633))))),
inference(variable_rename,[status(thm)],[aLIFTu_CMUL]) ).
cnf(c_0_26,plain,
s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X1))),s(real,i(s(fun(num,real),realu_ofu_num),s(num,i(s(fun(num,num),numeral),s(num,i(s(fun(num,num),bit1),s(num,u_0))))))))) = s(real,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,negated_conjecture,
s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),i(s(fun(real,fun(cart(real,n10),cart(real,n10))),r_),s(real,esk3826_0))),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(int,real),realu_ofu_int),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(ind0,num),mku_num),s(ind0,i(s(fun(ind0,ind0),indu_suc),s(ind0,i(s(fun(num,ind0),destu_num),s(num,u_0))))))))))))))) != s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,esk3826_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22]),c_0_23]),c_0_24]) ).
cnf(c_0_28,plain,
s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X1))),s(real,X2))))) = s(cart(real,n10),i(s(fun(cart(real,n10),cart(real,n10)),i(s(fun(real,fun(cart(real,n10),cart(real,n10))),r_),s(real,X1))),s(cart(real,n10),i(s(fun(real,cart(real,n10)),lift),s(real,X2))))),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,plain,
s(real,i(s(fun(real,real),i(s(fun(real,fun(real,real)),realu_mul),s(real,X1))),s(real,i(s(fun(int,real),realu_ofu_int),s(int,i(s(fun(num,int),intu_ofu_num),s(num,i(s(fun(ind0,num),mku_num),s(ind0,i(s(fun(ind0,ind0),indu_suc),s(ind0,i(s(fun(num,ind0),destu_num),s(num,u_0))))))))))))) = s(real,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_20]),c_0_21]),c_0_22]),c_0_23]),c_0_17]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO456+1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n004.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 16:26:34 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.89/3.66 % Version: 3.5.1
% 14.89/3.66 % Preprocessing class: FMLMSMSLSSSNFFN.
% 14.89/3.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.89/3.66 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 14.89/3.66 % Starting new_bool_3 with 600s (2) cores
% 14.89/3.66 % Starting new_bool_1 with 600s (2) cores
% 14.89/3.66 % Starting sh5l with 300s (1) cores
% 14.89/3.66 % G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with pid 1088163 completed with status 0
% 14.89/3.66 % Result found by G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN
% 14.89/3.66 % Preprocessing class: FMLMSMSLSSSNFFN.
% 14.89/3.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.89/3.66 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 14.89/3.66 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.89/3.66 % No SInE strategy applied
% 14.89/3.66 % Search class: FGHSM-SMLM33-DFFFFFNN
% 14.89/3.66 % Scheduled 7 strats onto 3 cores with 899 seconds (899 total)
% 14.89/3.66 % Starting SubtermCWHack with 81s (1) cores
% 14.89/3.66 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 90s (1) cores
% 14.89/3.66 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 81s (1) cores
% 14.89/3.66 % U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 1088173 completed with status 0
% 14.89/3.66 % Result found by U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 14.89/3.66 % Preprocessing class: FMLMSMSLSSSNFFN.
% 14.89/3.66 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 14.89/3.66 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 900s (3) cores
% 14.89/3.66 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 14.89/3.66 % No SInE strategy applied
% 14.89/3.66 % Search class: FGHSM-SMLM33-DFFFFFNN
% 14.89/3.66 % Scheduled 7 strats onto 3 cores with 899 seconds (899 total)
% 14.89/3.66 % Starting SubtermCWHack with 81s (1) cores
% 14.89/3.66 % Starting G-E--_208_C18C--_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 90s (1) cores
% 14.89/3.66 % Starting U----_206e_00_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 81s (1) cores
% 14.89/3.66 % Preprocessing time : 0.498 s
% 14.89/3.66 % Presaturation interreduction done
% 14.89/3.66
% 14.89/3.66 % Proof found!
% 14.89/3.66 % SZS status Theorem
% 14.89/3.66 % SZS output start CNFRefutation
% See solution above
% 14.89/3.66 % Parsed axioms : 3237
% 14.89/3.66 % Removed by relevancy pruning/SinE : 0
% 14.89/3.66 % Initial clauses : 9121
% 14.89/3.66 % Removed in clause preprocessing : 328
% 14.89/3.66 % Initial clauses in saturation : 8793
% 14.89/3.66 % Processed clauses : 2757
% 14.89/3.66 % ...of these trivial : 103
% 14.89/3.66 % ...subsumed : 167
% 14.89/3.66 % ...remaining for further processing : 2487
% 14.89/3.66 % Other redundant clauses eliminated : 0
% 14.89/3.66 % Clauses deleted for lack of memory : 0
% 14.89/3.66 % Backward-subsumed : 9
% 14.89/3.66 % Backward-rewritten : 334
% 14.89/3.66 % Generated clauses : 0
% 14.89/3.66 % ...of the previous two non-redundant : 266
% 14.89/3.66 % ...aggressively subsumed : 0
% 14.89/3.66 % Contextual simplify-reflections : 5
% 14.89/3.66 % Paramodulations : 0
% 14.89/3.66 % Factorizations : 0
% 14.89/3.66 % NegExts : 0
% 14.89/3.66 % Equation resolutions : 0
% 14.89/3.66 % Disequality decompositions : 0
% 14.89/3.66 % Total rewrite steps : 3035
% 14.89/3.66 % ...of those cached : 2098
% 14.89/3.66 % Propositional unsat checks : 0
% 14.89/3.66 % Propositional check models : 0
% 14.89/3.66 % Propositional check unsatisfiable : 0
% 14.89/3.66 % Propositional clauses : 0
% 14.89/3.66 % Propositional clauses after purity: 0
% 14.89/3.66 % Propositional unsat core size : 0
% 14.89/3.66 % Propositional preprocessing time : 0.000
% 14.89/3.66 % Propositional encoding time : 0.000
% 14.89/3.66 % Propositional solver time : 0.000
% 14.89/3.66 % Success case prop preproc time : 0.000
% 14.89/3.66 % Success case prop encoding time : 0.000
% 14.89/3.66 % Success case prop solver time : 0.000
% 14.89/3.66 % Current number of processed clauses : 2144
% 14.89/3.66 % Positive orientable unit clauses : 573
% 14.89/3.66 % Positive unorientable unit clauses: 59
% 14.89/3.66 % Negative unit clauses : 17
% 14.89/3.66 % Non-unit-clauses : 1495
% 14.89/3.66 % Current number of unprocessed clauses: 6302
% 14.89/3.66 % ...number of literals in the above : 42745
% 14.89/3.66 % Current number of archived formulas : 0
% 14.89/3.66 % Current number of archived clauses : 343
% 14.89/3.66 % Clause-clause subsumption calls (NU) : 209836
% 14.89/3.66 % Rec. Clause-clause subsumption calls : 148450
% 14.89/3.66 % Non-unit clause-clause subsumptions : 160
% 14.89/3.66 % Unit Clause-clause subsumption calls : 308
% 14.89/3.66 % Rewrite failures with RHS unbound : 0
% 14.89/3.66 % BW rewrite match attempts : 264384
% 14.89/3.66 % BW rewrite match successes : 3889
% 14.89/3.66 % Condensation attempts : 0
% 14.89/3.66 % Condensation successes : 0
% 14.89/3.66 % Termbank termtop insertions : 5827662
% 14.89/3.66 % Search garbage collected termcells : 175518
% 14.89/3.66
% 14.89/3.66 % -------------------------------------------------
% 14.89/3.66 % User time : 2.389 s
% 14.89/3.66 % System time : 0.125 s
% 14.89/3.66 % Total time : 2.514 s
% 14.89/3.66 % Maximum resident set size: 67764 pages
% 14.89/3.66
% 14.89/3.66 % -------------------------------------------------
% 14.89/3.66 % User time : 4.953 s
% 14.89/3.66 % System time : 0.344 s
% 14.89/3.66 % Total time : 5.297 s
% 14.89/3.66 % Maximum resident set size: 14592 pages
% 14.89/3.66 % E exiting
%------------------------------------------------------------------------------