TSTP Solution File: COL090-1 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : COL090-1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.7nZXoB22tm true
% Computer : n021.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 : Wed Aug 30 18:34:50 EDT 2023
% Result : Unsatisfiable 3.29s 1.19s
% Output : Refutation 3.29s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL090-1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.7nZXoB22tm true
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Aug 27 04:28:12 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running portfolio for 300 s
% 0.14/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.35 % Number of cores: 8
% 0.14/0.35 % Python version: Python 3.6.8
% 0.14/0.35 % Running in FO mode
% 0.21/0.65 % Total configuration time : 435
% 0.21/0.65 % Estimated wc time : 1092
% 0.21/0.65 % Estimated cpu time (7 cpus) : 156.0
% 0.21/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.21/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.21/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.21/0.78 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.21/0.79 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 3.29/1.19 % Solved by fo/fo4.sh.
% 3.29/1.19 % done 434 iterations in 0.300s
% 3.29/1.19 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 3.29/1.19 % SZS output start Refutation
% 3.29/1.19 thf('#_fresh_sk2_type', type, '#_fresh_sk2': $i > $i).
% 3.29/1.19 thf(ap_contractE_sk1q_type, type, ap_contractE_sk1q: $i > $i > $i > $i).
% 3.29/1.19 thf(ap_contractE_sk3q_type, type, ap_contractE_sk3q: $i > $i > $i > $i).
% 3.29/1.19 thf(ap_contractE_sk2q_type, type, ap_contractE_sk2q: $i > $i > $i > $i).
% 3.29/1.19 thf(ap_contractE_c3_type, type, ap_contractE_c3: $i > $i > $i > $o).
% 3.29/1.19 thf(ap_contractE_sk1p_type, type, ap_contractE_sk1p: $i > $i > $i > $i).
% 3.29/1.19 thf(comb_app_type, type, comb_app: $i > $i > $i).
% 3.29/1.19 thf(contract_type, type, contract: $i).
% 3.29/1.19 thf(r_type, type, r: $i).
% 3.29/1.19 thf(ap_contractE_c1_type, type, ap_contractE_c1: $i > $i > $i > $o).
% 3.29/1.19 thf(ap_contractE_c2_type, type, ap_contractE_c2: $i > $i > $i > $o).
% 3.29/1.19 thf('#_fresh_sk1_type', type, '#_fresh_sk1': $i > $i).
% 3.29/1.19 thf(combS_type, type, combS: $i).
% 3.29/1.19 thf(member_type, type, member: $i > $i > $o).
% 3.29/1.19 thf(pair_type, type, pair: $i > $i > $i).
% 3.29/1.19 thf(combK_type, type, combK: $i).
% 3.29/1.19 thf(ap_contractE_c4_type, type, ap_contractE_c4: $i > $i > $i > $o).
% 3.29/1.19 thf(i_contract_E, conjecture,
% 3.29/1.19 (~( member @
% 3.29/1.19 ( pair @ ( comb_app @ ( comb_app @ combS @ combK ) @ combK ) @ r ) @
% 3.29/1.19 contract ))).
% 3.29/1.19 thf(zf_stmt_0, negated_conjecture,
% 3.29/1.19 (member @
% 3.29/1.19 ( pair @ ( comb_app @ ( comb_app @ combS @ combK ) @ combK ) @ r ) @
% 3.29/1.19 contract),
% 3.29/1.19 inference('cnf.neg', [status(esa)], [i_contract_E])).
% 3.29/1.19 thf(zip_derived_cl31, plain,
% 3.29/1.19 ( (member @
% 3.29/1.19 (pair @ (comb_app @ (comb_app @ combS @ combK) @ combK) @ r) @
% 3.29/1.19 contract)),
% 3.29/1.19 inference('cnf', [status(esa)], [zf_stmt_0])).
% 3.29/1.19 thf(ap_contractE1, axiom,
% 3.29/1.19 (( ~( member @ ( pair @ ( comb_app @ P @ Q ) @ R ) @ contract ) ) |
% 3.29/1.19 ( ap_contractE_c1 @ P @ Q @ R ) | ( ap_contractE_c2 @ P @ Q @ R ) |
% 3.29/1.19 ( ap_contractE_c3 @ P @ Q @ R ) | ( ap_contractE_c4 @ P @ Q @ R ))).
% 3.29/1.19 thf(zip_derived_cl14, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.29/1.19 (~ (member @ (pair @ (comb_app @ X0 @ X1) @ X2) @ contract)
% 3.29/1.19 | (ap_contractE_c1 @ X0 @ X1 @ X2)
% 3.29/1.19 | (ap_contractE_c2 @ X0 @ X1 @ X2)
% 3.29/1.19 | (ap_contractE_c3 @ X0 @ X1 @ X2)
% 3.29/1.19 | (ap_contractE_c4 @ X0 @ X1 @ X2))),
% 3.29/1.19 inference('cnf', [status(esa)], [ap_contractE1])).
% 3.29/1.19 thf(zip_derived_cl69, plain,
% 3.29/1.19 (( (ap_contractE_c4 @ (comb_app @ combS @ combK) @ combK @ r)
% 3.29/1.19 | (ap_contractE_c3 @ (comb_app @ combS @ combK) @ combK @ r)
% 3.29/1.19 | (ap_contractE_c2 @ (comb_app @ combS @ combK) @ combK @ r)
% 3.29/1.19 | (ap_contractE_c1 @ (comb_app @ combS @ combK) @ combK @ r))),
% 3.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl31, zip_derived_cl14])).
% 3.29/1.19 thf(ap_contractE13, axiom,
% 3.29/1.19 (( ~( ap_contractE_c4 @ P @ Q @ R ) ) |
% 3.29/1.19 ( member @ ( pair @ Q @ ( ap_contractE_sk3q @ P @ Q @ R ) ) @ contract ))).
% 3.29/1.19 thf(zip_derived_cl26, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.29/1.19 (~ (ap_contractE_c4 @ X0 @ X1 @ X2)
% 3.29/1.19 | (member @ (pair @ X1 @ (ap_contractE_sk3q @ X0 @ X1 @ X2)) @
% 3.29/1.19 contract))),
% 3.29/1.19 inference('cnf', [status(esa)], [ap_contractE13])).
% 3.29/1.19 thf(k_contractE, axiom, (~( member @ ( pair @ combK @ R ) @ contract ))).
% 3.29/1.19 thf(zip_derived_cl29, plain,
% 3.29/1.19 (![X0 : $i]: ~ (member @ (pair @ combK @ X0) @ contract)),
% 3.29/1.19 inference('cnf', [status(esa)], [k_contractE])).
% 3.29/1.19 thf(zip_derived_cl64, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i]: ~ (ap_contractE_c4 @ X1 @ combK @ X0)),
% 3.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl29])).
% 3.29/1.19 thf(zip_derived_cl95, plain,
% 3.29/1.19 (( (ap_contractE_c3 @ (comb_app @ combS @ combK) @ combK @ r)
% 3.29/1.19 | (ap_contractE_c2 @ (comb_app @ combS @ combK) @ combK @ r)
% 3.29/1.19 | (ap_contractE_c1 @ (comb_app @ combS @ combK) @ combK @ r))),
% 3.29/1.19 inference('demod', [status(thm)], [zip_derived_cl69, zip_derived_cl64])).
% 3.29/1.19 thf(ap_contractE4, axiom,
% 3.29/1.19 (( ~( ap_contractE_c1 @ P @ Q @ R ) ) |
% 3.29/1.19 ( ( P ) = ( comb_app @ combK @ R ) ))).
% 3.29/1.19 thf(zip_derived_cl17, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.29/1.19 (~ (ap_contractE_c1 @ X0 @ X1 @ X2) | ((X0) = (comb_app @ combK @ X2)))),
% 3.29/1.19 inference('cnf', [status(esa)], [ap_contractE4])).
% 3.29/1.19 thf(zip_derived_cl98, plain,
% 3.29/1.19 (( (ap_contractE_c2 @ (comb_app @ combS @ combK) @ combK @ r)
% 3.29/1.19 | (ap_contractE_c3 @ (comb_app @ combS @ combK) @ combK @ r)
% 3.29/1.19 | ((comb_app @ combS @ combK) = (comb_app @ combK @ r)))),
% 3.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl95, zip_derived_cl17])).
% 3.29/1.19 thf(zip_derived_cl98, plain,
% 3.29/1.19 (( (ap_contractE_c2 @ (comb_app @ combS @ combK) @ combK @ r)
% 3.29/1.19 | (ap_contractE_c3 @ (comb_app @ combS @ combK) @ combK @ r)
% 3.29/1.19 | ((comb_app @ combS @ combK) = (comb_app @ combK @ r)))),
% 3.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl95, zip_derived_cl17])).
% 3.29/1.19 thf(ap_contractE12, axiom,
% 3.29/1.19 (( ~( ap_contractE_c3 @ P @ Q @ R ) ) |
% 3.29/1.19 ( ( R ) = ( comb_app @ ( ap_contractE_sk2q @ P @ Q @ R ) @ Q ) ))).
% 3.29/1.19 thf(zip_derived_cl25, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.29/1.19 (~ (ap_contractE_c3 @ X0 @ X1 @ X2)
% 3.29/1.19 | ((X2) = (comb_app @ (ap_contractE_sk2q @ X0 @ X1 @ X2) @ X1)))),
% 3.29/1.19 inference('cnf', [status(esa)], [ap_contractE12])).
% 3.29/1.19 thf(app_app2, axiom,
% 3.29/1.19 (( ( comb_app @ P1 @ Q1 ) != ( comb_app @ P2 @ Q2 ) ) | ( ( Q1 ) = ( Q2 ) ))).
% 3.29/1.19 thf(zip_derived_cl4, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.29/1.19 (((comb_app @ X2 @ X3) != (comb_app @ X0 @ X1)) | ((X3) = (X1)))),
% 3.29/1.19 inference('cnf', [status(esa)], [app_app2])).
% 3.29/1.19 thf(zip_derived_cl35, plain,
% 3.29/1.19 (![X2 : $i, X3 : $i]: (('#_fresh_sk2' @ (comb_app @ X2 @ X3)) = (X3))),
% 3.29/1.19 inference('inj_rec', [status(thm)], [zip_derived_cl4])).
% 3.29/1.19 thf(zip_derived_cl48, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.29/1.19 ((('#_fresh_sk2' @ X0) = (X1)) | ~ (ap_contractE_c3 @ X2 @ X1 @ X0))),
% 3.29/1.19 inference('sup+', [status(thm)], [zip_derived_cl25, zip_derived_cl35])).
% 3.29/1.19 thf(zip_derived_cl109, plain,
% 3.29/1.19 ((((comb_app @ combS @ combK) = (comb_app @ combK @ r))
% 3.29/1.19 | (ap_contractE_c2 @ (comb_app @ combS @ combK) @ combK @ r)
% 3.29/1.19 | (('#_fresh_sk2' @ r) = (combK)))),
% 3.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl98, zip_derived_cl48])).
% 3.29/1.19 thf(ap_contractE9, axiom,
% 3.29/1.19 (( ~( ap_contractE_c2 @ P @ Q @ R ) ) |
% 3.29/1.19 ( ( P ) =
% 3.29/1.19 ( comb_app @
% 3.29/1.19 ( comb_app @ combS @ ( ap_contractE_sk1p @ P @ Q @ R ) ) @
% 3.29/1.19 ( ap_contractE_sk1q @ P @ Q @ R ) ) ))).
% 3.29/1.19 thf(zip_derived_cl22, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.29/1.19 (~ (ap_contractE_c2 @ X0 @ X1 @ X2)
% 3.29/1.19 | ((X0)
% 3.29/1.19 = (comb_app @
% 3.29/1.19 (comb_app @ combS @ (ap_contractE_sk1p @ X0 @ X1 @ X2)) @
% 3.29/1.19 (ap_contractE_sk1q @ X0 @ X1 @ X2))))),
% 3.29/1.19 inference('cnf', [status(esa)], [ap_contractE9])).
% 3.29/1.19 thf(app_app1, axiom,
% 3.29/1.19 (( ( comb_app @ P1 @ Q1 ) != ( comb_app @ P2 @ Q2 ) ) | ( ( P1 ) = ( P2 ) ))).
% 3.29/1.19 thf(zip_derived_cl3, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 3.29/1.19 (((comb_app @ X2 @ X3) != (comb_app @ X0 @ X1)) | ((X2) = (X0)))),
% 3.29/1.19 inference('cnf', [status(esa)], [app_app1])).
% 3.29/1.19 thf(zip_derived_cl33, plain,
% 3.29/1.19 (![X2 : $i, X3 : $i]: (('#_fresh_sk1' @ (comb_app @ X2 @ X3)) = (X2))),
% 3.29/1.19 inference('inj_rec', [status(thm)], [zip_derived_cl3])).
% 3.29/1.19 thf(zip_derived_cl82, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.29/1.19 ((('#_fresh_sk1' @ X0)
% 3.29/1.19 = (comb_app @ combS @ (ap_contractE_sk1p @ X0 @ X2 @ X1)))
% 3.29/1.19 | ~ (ap_contractE_c2 @ X0 @ X2 @ X1))),
% 3.29/1.19 inference('sup+', [status(thm)], [zip_derived_cl22, zip_derived_cl33])).
% 3.29/1.19 thf(s_app, axiom, (( combS ) != ( comb_app @ P @ Q ))).
% 3.29/1.19 thf(zip_derived_cl2, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i]: ((combS) != (comb_app @ X0 @ X1))),
% 3.29/1.19 inference('cnf', [status(esa)], [s_app])).
% 3.29/1.19 thf(zip_derived_cl250, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.29/1.19 (((combS) != ('#_fresh_sk1' @ X0))
% 3.29/1.19 | ~ (ap_contractE_c2 @ X0 @ X2 @ X1))),
% 3.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl82, zip_derived_cl2])).
% 3.29/1.19 thf(zip_derived_cl291, plain,
% 3.29/1.19 (((('#_fresh_sk2' @ r) = (combK))
% 3.29/1.19 | ((comb_app @ combS @ combK) = (comb_app @ combK @ r))
% 3.29/1.19 | ((combS) != ('#_fresh_sk1' @ (comb_app @ combS @ combK))))),
% 3.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl109, zip_derived_cl250])).
% 3.29/1.19 thf(zip_derived_cl33, plain,
% 3.29/1.19 (![X2 : $i, X3 : $i]: (('#_fresh_sk1' @ (comb_app @ X2 @ X3)) = (X2))),
% 3.29/1.19 inference('inj_rec', [status(thm)], [zip_derived_cl3])).
% 3.29/1.19 thf(zip_derived_cl295, plain,
% 3.29/1.19 (((('#_fresh_sk2' @ r) = (combK))
% 3.29/1.19 | ((comb_app @ combS @ combK) = (comb_app @ combK @ r))
% 3.29/1.19 | ((combS) != (combS)))),
% 3.29/1.19 inference('demod', [status(thm)], [zip_derived_cl291, zip_derived_cl33])).
% 3.29/1.19 thf(zip_derived_cl296, plain,
% 3.29/1.19 ((((comb_app @ combS @ combK) = (comb_app @ combK @ r))
% 3.29/1.19 | (('#_fresh_sk2' @ r) = (combK)))),
% 3.29/1.19 inference('simplify', [status(thm)], [zip_derived_cl295])).
% 3.29/1.19 thf(zip_derived_cl33, plain,
% 3.29/1.19 (![X2 : $i, X3 : $i]: (('#_fresh_sk1' @ (comb_app @ X2 @ X3)) = (X2))),
% 3.29/1.19 inference('inj_rec', [status(thm)], [zip_derived_cl3])).
% 3.29/1.19 thf(zip_derived_cl328, plain,
% 3.29/1.19 (((('#_fresh_sk1' @ (comb_app @ combS @ combK)) = (combK))
% 3.29/1.19 | (('#_fresh_sk2' @ r) = (combK)))),
% 3.29/1.19 inference('sup+', [status(thm)], [zip_derived_cl296, zip_derived_cl33])).
% 3.29/1.19 thf(zip_derived_cl33, plain,
% 3.29/1.19 (![X2 : $i, X3 : $i]: (('#_fresh_sk1' @ (comb_app @ X2 @ X3)) = (X2))),
% 3.29/1.19 inference('inj_rec', [status(thm)], [zip_derived_cl3])).
% 3.29/1.19 thf(zip_derived_cl338, plain,
% 3.29/1.19 ((((combS) = (combK)) | (('#_fresh_sk2' @ r) = (combK)))),
% 3.29/1.19 inference('demod', [status(thm)], [zip_derived_cl328, zip_derived_cl33])).
% 3.29/1.19 thf(k_s, axiom, (( combK ) != ( combS ))).
% 3.29/1.19 thf(zip_derived_cl0, plain, (((combK) != (combS))),
% 3.29/1.19 inference('cnf', [status(esa)], [k_s])).
% 3.29/1.19 thf(zip_derived_cl339, plain, ((('#_fresh_sk2' @ r) = (combK))),
% 3.29/1.19 inference('simplify_reflect-', [status(thm)],
% 3.29/1.19 [zip_derived_cl338, zip_derived_cl0])).
% 3.29/1.19 thf(zip_derived_cl339, plain, ((('#_fresh_sk2' @ r) = (combK))),
% 3.29/1.19 inference('simplify_reflect-', [status(thm)],
% 3.29/1.19 [zip_derived_cl338, zip_derived_cl0])).
% 3.29/1.19 thf(zip_derived_cl339, plain, ((('#_fresh_sk2' @ r) = (combK))),
% 3.29/1.19 inference('simplify_reflect-', [status(thm)],
% 3.29/1.19 [zip_derived_cl338, zip_derived_cl0])).
% 3.29/1.19 thf(zip_derived_cl339, plain, ((('#_fresh_sk2' @ r) = (combK))),
% 3.29/1.19 inference('simplify_reflect-', [status(thm)],
% 3.29/1.19 [zip_derived_cl338, zip_derived_cl0])).
% 3.29/1.19 thf(zip_derived_cl339, plain, ((('#_fresh_sk2' @ r) = (combK))),
% 3.29/1.19 inference('simplify_reflect-', [status(thm)],
% 3.29/1.19 [zip_derived_cl338, zip_derived_cl0])).
% 3.29/1.19 thf(zip_derived_cl339, plain, ((('#_fresh_sk2' @ r) = (combK))),
% 3.29/1.19 inference('simplify_reflect-', [status(thm)],
% 3.29/1.19 [zip_derived_cl338, zip_derived_cl0])).
% 3.29/1.19 thf(zip_derived_cl358, plain,
% 3.29/1.19 (( (ap_contractE_c2 @ (comb_app @ combS @ ('#_fresh_sk2' @ r)) @
% 3.29/1.19 ('#_fresh_sk2' @ r) @ r)
% 3.29/1.19 | (ap_contractE_c3 @ (comb_app @ combS @ ('#_fresh_sk2' @ r)) @
% 3.29/1.19 ('#_fresh_sk2' @ r) @ r)
% 3.29/1.19 | ((comb_app @ combS @ ('#_fresh_sk2' @ r))
% 3.29/1.19 = (comb_app @ ('#_fresh_sk2' @ r) @ r)))),
% 3.29/1.19 inference('demod', [status(thm)],
% 3.29/1.19 [zip_derived_cl98, zip_derived_cl339, zip_derived_cl339,
% 3.29/1.19 zip_derived_cl339, zip_derived_cl339, zip_derived_cl339,
% 3.29/1.19 zip_derived_cl339])).
% 3.29/1.19 thf(zip_derived_cl358, plain,
% 3.29/1.19 (( (ap_contractE_c2 @ (comb_app @ combS @ ('#_fresh_sk2' @ r)) @
% 3.29/1.19 ('#_fresh_sk2' @ r) @ r)
% 3.29/1.19 | (ap_contractE_c3 @ (comb_app @ combS @ ('#_fresh_sk2' @ r)) @
% 3.29/1.19 ('#_fresh_sk2' @ r) @ r)
% 3.29/1.19 | ((comb_app @ combS @ ('#_fresh_sk2' @ r))
% 3.29/1.19 = (comb_app @ ('#_fresh_sk2' @ r) @ r)))),
% 3.29/1.19 inference('demod', [status(thm)],
% 3.29/1.19 [zip_derived_cl98, zip_derived_cl339, zip_derived_cl339,
% 3.29/1.19 zip_derived_cl339, zip_derived_cl339, zip_derived_cl339,
% 3.29/1.19 zip_derived_cl339])).
% 3.29/1.19 thf(zip_derived_cl25, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.29/1.19 (~ (ap_contractE_c3 @ X0 @ X1 @ X2)
% 3.29/1.19 | ((X2) = (comb_app @ (ap_contractE_sk2q @ X0 @ X1 @ X2) @ X1)))),
% 3.29/1.19 inference('cnf', [status(esa)], [ap_contractE12])).
% 3.29/1.19 thf(zip_derived_cl33, plain,
% 3.29/1.19 (![X2 : $i, X3 : $i]: (('#_fresh_sk1' @ (comb_app @ X2 @ X3)) = (X2))),
% 3.29/1.19 inference('inj_rec', [status(thm)], [zip_derived_cl3])).
% 3.29/1.19 thf(zip_derived_cl47, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.29/1.19 ((('#_fresh_sk1' @ X0) = (ap_contractE_sk2q @ X2 @ X1 @ X0))
% 3.29/1.19 | ~ (ap_contractE_c3 @ X2 @ X1 @ X0))),
% 3.29/1.19 inference('sup+', [status(thm)], [zip_derived_cl25, zip_derived_cl33])).
% 3.29/1.19 thf(zip_derived_cl705, plain,
% 3.29/1.19 ((((comb_app @ combS @ ('#_fresh_sk2' @ r))
% 3.29/1.19 = (comb_app @ ('#_fresh_sk2' @ r) @ r))
% 3.29/1.19 | (ap_contractE_c2 @ (comb_app @ combS @ ('#_fresh_sk2' @ r)) @
% 3.29/1.19 ('#_fresh_sk2' @ r) @ r)
% 3.29/1.19 | (('#_fresh_sk1' @ r)
% 3.29/1.19 = (ap_contractE_sk2q @ (comb_app @ combS @ ('#_fresh_sk2' @ r)) @
% 3.29/1.19 ('#_fresh_sk2' @ r) @ r)))),
% 3.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl358, zip_derived_cl47])).
% 3.29/1.19 thf(ap_contractE8, axiom,
% 3.29/1.19 (( ~( ap_contractE_c2 @ P @ Q @ R ) ) |
% 3.29/1.19 ( ( R ) =
% 3.29/1.19 ( comb_app @
% 3.29/1.19 ( comb_app @ ( ap_contractE_sk1p @ P @ Q @ R ) @ Q ) @
% 3.29/1.19 ( comb_app @ ( ap_contractE_sk1q @ P @ Q @ R ) @ Q ) ) ))).
% 3.29/1.19 thf(zip_derived_cl21, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.29/1.19 (~ (ap_contractE_c2 @ X0 @ X1 @ X2)
% 3.29/1.19 | ((X2)
% 3.29/1.19 = (comb_app @
% 3.29/1.19 (comb_app @ (ap_contractE_sk1p @ X0 @ X1 @ X2) @ X1) @
% 3.29/1.19 (comb_app @ (ap_contractE_sk1q @ X0 @ X1 @ X2) @ X1))))),
% 3.29/1.19 inference('cnf', [status(esa)], [ap_contractE8])).
% 3.29/1.19 thf(zip_derived_cl35, plain,
% 3.29/1.19 (![X2 : $i, X3 : $i]: (('#_fresh_sk2' @ (comb_app @ X2 @ X3)) = (X3))),
% 3.29/1.19 inference('inj_rec', [status(thm)], [zip_derived_cl4])).
% 3.29/1.19 thf(zip_derived_cl139, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.29/1.19 ((('#_fresh_sk2' @ X0)
% 3.29/1.19 = (comb_app @ (ap_contractE_sk1q @ X2 @ X1 @ X0) @ X1))
% 3.29/1.19 | ~ (ap_contractE_c2 @ X2 @ X1 @ X0))),
% 3.29/1.19 inference('sup+', [status(thm)], [zip_derived_cl21, zip_derived_cl35])).
% 3.29/1.19 thf(k_app, axiom, (( combK ) != ( comb_app @ P @ Q ))).
% 3.29/1.19 thf(zip_derived_cl1, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i]: ((combK) != (comb_app @ X0 @ X1))),
% 3.29/1.19 inference('cnf', [status(esa)], [k_app])).
% 3.29/1.19 thf(zip_derived_cl339, plain, ((('#_fresh_sk2' @ r) = (combK))),
% 3.29/1.19 inference('simplify_reflect-', [status(thm)],
% 3.29/1.19 [zip_derived_cl338, zip_derived_cl0])).
% 3.29/1.19 thf(zip_derived_cl345, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i]: (('#_fresh_sk2' @ r) != (comb_app @ X0 @ X1))),
% 3.29/1.19 inference('demod', [status(thm)], [zip_derived_cl1, zip_derived_cl339])).
% 3.29/1.19 thf(zip_derived_cl637, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.29/1.19 ((('#_fresh_sk2' @ r) != ('#_fresh_sk2' @ X0))
% 3.29/1.19 | ~ (ap_contractE_c2 @ X2 @ X1 @ X0))),
% 3.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl139, zip_derived_cl345])).
% 3.29/1.19 thf(zip_derived_cl1011, plain,
% 3.29/1.19 (((('#_fresh_sk1' @ r)
% 3.29/1.19 = (ap_contractE_sk2q @ (comb_app @ combS @ ('#_fresh_sk2' @ r)) @
% 3.29/1.19 ('#_fresh_sk2' @ r) @ r))
% 3.29/1.19 | ((comb_app @ combS @ ('#_fresh_sk2' @ r))
% 3.29/1.19 = (comb_app @ ('#_fresh_sk2' @ r) @ r))
% 3.29/1.19 | (('#_fresh_sk2' @ r) != ('#_fresh_sk2' @ r)))),
% 3.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl705, zip_derived_cl637])).
% 3.29/1.19 thf(zip_derived_cl1040, plain,
% 3.29/1.19 ((((comb_app @ combS @ ('#_fresh_sk2' @ r))
% 3.29/1.19 = (comb_app @ ('#_fresh_sk2' @ r) @ r))
% 3.29/1.19 | (('#_fresh_sk1' @ r)
% 3.29/1.19 = (ap_contractE_sk2q @ (comb_app @ combS @ ('#_fresh_sk2' @ r)) @
% 3.29/1.19 ('#_fresh_sk2' @ r) @ r)))),
% 3.29/1.19 inference('simplify', [status(thm)], [zip_derived_cl1011])).
% 3.29/1.19 thf(ap_contractE10, axiom,
% 3.29/1.19 (( ~( ap_contractE_c3 @ P @ Q @ R ) ) |
% 3.29/1.19 ( member @ ( pair @ P @ ( ap_contractE_sk2q @ P @ Q @ R ) ) @ contract ))).
% 3.29/1.19 thf(zip_derived_cl23, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.29/1.19 (~ (ap_contractE_c3 @ X0 @ X1 @ X2)
% 3.29/1.19 | (member @ (pair @ X0 @ (ap_contractE_sk2q @ X0 @ X1 @ X2)) @
% 3.29/1.19 contract))),
% 3.29/1.19 inference('cnf', [status(esa)], [ap_contractE10])).
% 3.29/1.19 thf(zip_derived_cl1120, plain,
% 3.29/1.19 (( (member @
% 3.29/1.19 (pair @ (comb_app @ combS @ ('#_fresh_sk2' @ r)) @
% 3.29/1.19 ('#_fresh_sk1' @ r)) @
% 3.29/1.19 contract)
% 3.29/1.19 | ((comb_app @ combS @ ('#_fresh_sk2' @ r))
% 3.29/1.19 = (comb_app @ ('#_fresh_sk2' @ r) @ r))
% 3.29/1.19 | ~ (ap_contractE_c3 @ (comb_app @ combS @ ('#_fresh_sk2' @ r)) @
% 3.29/1.19 ('#_fresh_sk2' @ r) @ r))),
% 3.29/1.19 inference('sup+', [status(thm)], [zip_derived_cl1040, zip_derived_cl23])).
% 3.29/1.19 thf(zip_derived_cl1131, plain,
% 3.29/1.19 ((((comb_app @ combS @ ('#_fresh_sk2' @ r))
% 3.29/1.19 = (comb_app @ ('#_fresh_sk2' @ r) @ r))
% 3.29/1.19 | (ap_contractE_c2 @ (comb_app @ combS @ ('#_fresh_sk2' @ r)) @
% 3.29/1.19 ('#_fresh_sk2' @ r) @ r)
% 3.29/1.19 | ((comb_app @ combS @ ('#_fresh_sk2' @ r))
% 3.29/1.19 = (comb_app @ ('#_fresh_sk2' @ r) @ r))
% 3.29/1.19 | (member @
% 3.29/1.19 (pair @ (comb_app @ combS @ ('#_fresh_sk2' @ r)) @
% 3.29/1.19 ('#_fresh_sk1' @ r)) @
% 3.29/1.19 contract))),
% 3.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl358, zip_derived_cl1120])).
% 3.29/1.19 thf(zip_derived_cl1132, plain,
% 3.29/1.19 (( (member @
% 3.29/1.19 (pair @ (comb_app @ combS @ ('#_fresh_sk2' @ r)) @
% 3.29/1.19 ('#_fresh_sk1' @ r)) @
% 3.29/1.19 contract)
% 3.29/1.19 | (ap_contractE_c2 @ (comb_app @ combS @ ('#_fresh_sk2' @ r)) @
% 3.29/1.19 ('#_fresh_sk2' @ r) @ r)
% 3.29/1.19 | ((comb_app @ combS @ ('#_fresh_sk2' @ r))
% 3.29/1.19 = (comb_app @ ('#_fresh_sk2' @ r) @ r)))),
% 3.29/1.19 inference('simplify', [status(thm)], [zip_derived_cl1131])).
% 3.29/1.19 thf(zip_derived_cl14, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.29/1.19 (~ (member @ (pair @ (comb_app @ X0 @ X1) @ X2) @ contract)
% 3.29/1.19 | (ap_contractE_c1 @ X0 @ X1 @ X2)
% 3.29/1.19 | (ap_contractE_c2 @ X0 @ X1 @ X2)
% 3.29/1.19 | (ap_contractE_c3 @ X0 @ X1 @ X2)
% 3.29/1.19 | (ap_contractE_c4 @ X0 @ X1 @ X2))),
% 3.29/1.19 inference('cnf', [status(esa)], [ap_contractE1])).
% 3.29/1.19 thf(zip_derived_cl1214, plain,
% 3.29/1.19 ((((comb_app @ combS @ ('#_fresh_sk2' @ r))
% 3.29/1.19 = (comb_app @ ('#_fresh_sk2' @ r) @ r))
% 3.29/1.19 | (ap_contractE_c2 @ (comb_app @ combS @ ('#_fresh_sk2' @ r)) @
% 3.29/1.19 ('#_fresh_sk2' @ r) @ r)
% 3.29/1.19 | (ap_contractE_c4 @ combS @ ('#_fresh_sk2' @ r) @ ('#_fresh_sk1' @ r))
% 3.29/1.19 | (ap_contractE_c3 @ combS @ ('#_fresh_sk2' @ r) @ ('#_fresh_sk1' @ r))
% 3.29/1.19 | (ap_contractE_c2 @ combS @ ('#_fresh_sk2' @ r) @ ('#_fresh_sk1' @ r))
% 3.29/1.19 | (ap_contractE_c1 @ combS @ ('#_fresh_sk2' @ r) @ ('#_fresh_sk1' @ r)))),
% 3.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl1132, zip_derived_cl14])).
% 3.29/1.19 thf(zip_derived_cl64, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i]: ~ (ap_contractE_c4 @ X1 @ combK @ X0)),
% 3.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl29])).
% 3.29/1.19 thf(zip_derived_cl339, plain, ((('#_fresh_sk2' @ r) = (combK))),
% 3.29/1.19 inference('simplify_reflect-', [status(thm)],
% 3.29/1.19 [zip_derived_cl338, zip_derived_cl0])).
% 3.29/1.19 thf(zip_derived_cl354, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i]: ~ (ap_contractE_c4 @ X1 @ ('#_fresh_sk2' @ r) @ X0)),
% 3.29/1.19 inference('demod', [status(thm)], [zip_derived_cl64, zip_derived_cl339])).
% 3.29/1.19 thf(zip_derived_cl23, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.29/1.19 (~ (ap_contractE_c3 @ X0 @ X1 @ X2)
% 3.29/1.19 | (member @ (pair @ X0 @ (ap_contractE_sk2q @ X0 @ X1 @ X2)) @
% 3.29/1.19 contract))),
% 3.29/1.19 inference('cnf', [status(esa)], [ap_contractE10])).
% 3.29/1.19 thf(s_contractE, axiom, (~( member @ ( pair @ combS @ R ) @ contract ))).
% 3.29/1.19 thf(zip_derived_cl30, plain,
% 3.29/1.19 (![X0 : $i]: ~ (member @ (pair @ combS @ X0) @ contract)),
% 3.29/1.19 inference('cnf', [status(esa)], [s_contractE])).
% 3.29/1.19 thf(zip_derived_cl63, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i]: ~ (ap_contractE_c3 @ combS @ X1 @ X0)),
% 3.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl23, zip_derived_cl30])).
% 3.29/1.19 thf(zip_derived_cl1215, plain,
% 3.29/1.19 ((((comb_app @ combS @ ('#_fresh_sk2' @ r))
% 3.29/1.19 = (comb_app @ ('#_fresh_sk2' @ r) @ r))
% 3.29/1.19 | (ap_contractE_c2 @ (comb_app @ combS @ ('#_fresh_sk2' @ r)) @
% 3.29/1.19 ('#_fresh_sk2' @ r) @ r)
% 3.29/1.19 | (ap_contractE_c2 @ combS @ ('#_fresh_sk2' @ r) @ ('#_fresh_sk1' @ r))
% 3.29/1.19 | (ap_contractE_c1 @ combS @ ('#_fresh_sk2' @ r) @ ('#_fresh_sk1' @ r)))),
% 3.29/1.19 inference('demod', [status(thm)],
% 3.29/1.19 [zip_derived_cl1214, zip_derived_cl354, zip_derived_cl63])).
% 3.29/1.19 thf(zip_derived_cl637, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.29/1.19 ((('#_fresh_sk2' @ r) != ('#_fresh_sk2' @ X0))
% 3.29/1.19 | ~ (ap_contractE_c2 @ X2 @ X1 @ X0))),
% 3.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl139, zip_derived_cl345])).
% 3.29/1.19 thf(zip_derived_cl1336, plain,
% 3.29/1.19 (( (ap_contractE_c1 @ combS @ ('#_fresh_sk2' @ r) @ ('#_fresh_sk1' @ r))
% 3.29/1.19 | (ap_contractE_c2 @ combS @ ('#_fresh_sk2' @ r) @ ('#_fresh_sk1' @ r))
% 3.29/1.19 | ((comb_app @ combS @ ('#_fresh_sk2' @ r))
% 3.29/1.19 = (comb_app @ ('#_fresh_sk2' @ r) @ r))
% 3.29/1.19 | (('#_fresh_sk2' @ r) != ('#_fresh_sk2' @ r)))),
% 3.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl1215, zip_derived_cl637])).
% 3.29/1.19 thf(zip_derived_cl1370, plain,
% 3.29/1.19 ((((comb_app @ combS @ ('#_fresh_sk2' @ r))
% 3.29/1.19 = (comb_app @ ('#_fresh_sk2' @ r) @ r))
% 3.29/1.19 | (ap_contractE_c2 @ combS @ ('#_fresh_sk2' @ r) @ ('#_fresh_sk1' @ r))
% 3.29/1.19 | (ap_contractE_c1 @ combS @ ('#_fresh_sk2' @ r) @ ('#_fresh_sk1' @ r)))),
% 3.29/1.19 inference('simplify', [status(thm)], [zip_derived_cl1336])).
% 3.29/1.19 thf(zip_derived_cl17, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.29/1.19 (~ (ap_contractE_c1 @ X0 @ X1 @ X2) | ((X0) = (comb_app @ combK @ X2)))),
% 3.29/1.19 inference('cnf', [status(esa)], [ap_contractE4])).
% 3.29/1.19 thf(zip_derived_cl339, plain, ((('#_fresh_sk2' @ r) = (combK))),
% 3.29/1.19 inference('simplify_reflect-', [status(thm)],
% 3.29/1.19 [zip_derived_cl338, zip_derived_cl0])).
% 3.29/1.19 thf(zip_derived_cl348, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.29/1.19 (~ (ap_contractE_c1 @ X0 @ X1 @ X2)
% 3.29/1.19 | ((X0) = (comb_app @ ('#_fresh_sk2' @ r) @ X2)))),
% 3.29/1.19 inference('demod', [status(thm)], [zip_derived_cl17, zip_derived_cl339])).
% 3.29/1.19 thf(zip_derived_cl1429, plain,
% 3.29/1.19 (( (ap_contractE_c2 @ combS @ ('#_fresh_sk2' @ r) @ ('#_fresh_sk1' @ r))
% 3.29/1.19 | ((comb_app @ combS @ ('#_fresh_sk2' @ r))
% 3.29/1.19 = (comb_app @ ('#_fresh_sk2' @ r) @ r))
% 3.29/1.19 | ((combS) = (comb_app @ ('#_fresh_sk2' @ r) @ ('#_fresh_sk1' @ r))))),
% 3.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl1370, zip_derived_cl348])).
% 3.29/1.19 thf(zip_derived_cl2, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i]: ((combS) != (comb_app @ X0 @ X1))),
% 3.29/1.19 inference('cnf', [status(esa)], [s_app])).
% 3.29/1.19 thf(zip_derived_cl1431, plain,
% 3.29/1.19 (( (ap_contractE_c2 @ combS @ ('#_fresh_sk2' @ r) @ ('#_fresh_sk1' @ r))
% 3.29/1.19 | ((comb_app @ combS @ ('#_fresh_sk2' @ r))
% 3.29/1.19 = (comb_app @ ('#_fresh_sk2' @ r) @ r)))),
% 3.29/1.19 inference('simplify_reflect-', [status(thm)],
% 3.29/1.19 [zip_derived_cl1429, zip_derived_cl2])).
% 3.29/1.19 thf(zip_derived_cl22, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.29/1.19 (~ (ap_contractE_c2 @ X0 @ X1 @ X2)
% 3.29/1.19 | ((X0)
% 3.29/1.19 = (comb_app @
% 3.29/1.19 (comb_app @ combS @ (ap_contractE_sk1p @ X0 @ X1 @ X2)) @
% 3.29/1.19 (ap_contractE_sk1q @ X0 @ X1 @ X2))))),
% 3.29/1.19 inference('cnf', [status(esa)], [ap_contractE9])).
% 3.29/1.19 thf(zip_derived_cl2, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i]: ((combS) != (comb_app @ X0 @ X1))),
% 3.29/1.19 inference('cnf', [status(esa)], [s_app])).
% 3.29/1.19 thf(zip_derived_cl73, plain,
% 3.29/1.19 (![X0 : $i, X1 : $i, X2 : $i]:
% 3.29/1.19 (((combS) != (X0)) | ~ (ap_contractE_c2 @ X0 @ X2 @ X1))),
% 3.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl22, zip_derived_cl2])).
% 3.29/1.19 thf(zip_derived_cl1460, plain,
% 3.29/1.19 ((((comb_app @ combS @ ('#_fresh_sk2' @ r))
% 3.29/1.19 = (comb_app @ ('#_fresh_sk2' @ r) @ r))
% 3.29/1.19 | ((combS) != (combS)))),
% 3.29/1.19 inference('sup-', [status(thm)], [zip_derived_cl1431, zip_derived_cl73])).
% 3.29/1.19 thf(zip_derived_cl1487, plain,
% 3.29/1.19 (((comb_app @ combS @ ('#_fresh_sk2' @ r))
% 3.29/1.19 = (comb_app @ ('#_fresh_sk2' @ r) @ r))),
% 3.29/1.19 inference('simplify', [status(thm)], [zip_derived_cl1460])).
% 3.29/1.19 thf(zip_derived_cl33, plain,
% 3.29/1.19 (![X2 : $i, X3 : $i]: (('#_fresh_sk1' @ (comb_app @ X2 @ X3)) = (X2))),
% 3.29/1.19 inference('inj_rec', [status(thm)], [zip_derived_cl3])).
% 3.29/1.19 thf(zip_derived_cl1501, plain,
% 3.29/1.19 ((('#_fresh_sk1' @ (comb_app @ combS @ ('#_fresh_sk2' @ r)))
% 3.29/1.19 = ('#_fresh_sk2' @ r))),
% 3.29/1.19 inference('sup+', [status(thm)], [zip_derived_cl1487, zip_derived_cl33])).
% 3.29/1.19 thf(zip_derived_cl33, plain,
% 3.29/1.19 (![X2 : $i, X3 : $i]: (('#_fresh_sk1' @ (comb_app @ X2 @ X3)) = (X2))),
% 3.29/1.19 inference('inj_rec', [status(thm)], [zip_derived_cl3])).
% 3.29/1.19 thf(zip_derived_cl1517, plain, (((combS) = ('#_fresh_sk2' @ r))),
% 3.29/1.19 inference('demod', [status(thm)], [zip_derived_cl1501, zip_derived_cl33])).
% 3.29/1.19 thf(zip_derived_cl0, plain, (((combK) != (combS))),
% 3.29/1.19 inference('cnf', [status(esa)], [k_s])).
% 3.29/1.19 thf(zip_derived_cl339, plain, ((('#_fresh_sk2' @ r) = (combK))),
% 3.29/1.19 inference('simplify_reflect-', [status(thm)],
% 3.29/1.19 [zip_derived_cl338, zip_derived_cl0])).
% 3.29/1.19 thf(zip_derived_cl344, plain, ((('#_fresh_sk2' @ r) != (combS))),
% 3.29/1.19 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl339])).
% 3.29/1.19 thf(zip_derived_cl1518, plain, ($false),
% 3.29/1.19 inference('simplify_reflect-', [status(thm)],
% 3.29/1.19 [zip_derived_cl1517, zip_derived_cl344])).
% 3.29/1.19
% 3.29/1.19 % SZS output end Refutation
% 3.29/1.19
% 3.29/1.19
% 3.69/1.19 % Terminating...
% 3.88/1.26 % Runner terminated.
% 3.88/1.27 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------